To answer these questions, or at least present some reasonably useful observations, I scanned all the Bond films and made a note of the scenes in which M appears. I began to record the length of each scene, but stopped early in the series owing to lack of time, and so for the purpose of this analysis, screen time is measured by the number of scenes in which M appears. Without re-watching the films in their entirety, it's highly likely that I've missed the odd scene here and there, but the general trends should be clear.
The first four films in the series show a gradual rise in the number of M's scenes. Starting with a single appearance in Dr No to brief Sean Connery's Bond and order him to take the Walther PPK, M, played by Bernard Lee, has two appearances in From Russia with Love – a briefing and a scene in which he listens to a recording of Bond's questioning of Tatiana Romanova – and three appearances in Goldfinger (a briefing, a meeting at the Bank of England and a mid-mission update). In Thunderball, M has four scenes, including two scenes in a situation or war room. M has fewer scenes in You Only Live Twice, but this reduction is more than made up for in On Her Majesty's Secret Service, in which he has six scenes, including a scene at his home. The number of scenes is exceptional, however, and in Diamonds Are Forever returns to a number approaching the average (4.8 scenes per film).
Apart from Live and Let Die, M's appearances during Roger Moore's tenure are remarkably consistent in structure and function. Films from The Man With The Golden Gun (1974) through to A View To A Kill (1985) have four or five scenes, which follow a reasonably standard pattern. There is a briefing in M's office, followed by a second meeting in response to new information or, in M's view, some foolhardy action by Bond. M is then seen outside secret service headquarters to meet Bond at an arranged rendezvous (such as Checkpoint Charlie in Octopussy, the first film for Robert Brown as M) or at a regional headquarters (for instance in Brazil in Moonraker), before finally appearing at the mission's conclusion to congratulate Bond or explain Bond's absence (usually to General Gogol). There are, of course, variations to this pattern, but overall the structure of M's scenes have a similarity that the scenes in the films of the 1960s lack. For Your Eyes Only (1981), in which the role of M is shared by Q and chief-of-staff Tanner, and to a lesser extent Timothy Dalton's first Bond film, The Living Daylights (1987), also fit this model.
In Licence to Kill (1989), Bond operates outside the secret service and consequently M takes a marginal role in the film, appearing in just two scenes. On the face of it, the number of scenes in which Judy Dench's M appears during her tenure hovers around the average for the series. But no doubt M's screen time is greater than it had been during, for example, Roger Moore's era. Another significant development is that Judy Dench's M takes a much more direct role in Bond's mission compared with her predecessors, appearing in the situation room, regional or temporary headquarters or in the field more often than she appears in her office. There are nods to earlier tropes, however. The World Is Not Enough (1999) and Tomorrow Never Dies (1997), has the sort of humorous coda that would fit comfortably in any Roger Moore film. Both The World Is Not Enough and Skyfall are clear outliers, with the former's 11 scenes, and the latter's 20-odd scenes (including the final scene introducing Mallory as the new M). In these films, M is part of the narrative and naturally has a substantially increased presence.
While it could be claimed that M's enhanced and proactive role evident during the Pierce Brosnan and Daniel Craig eras has been driven more by Judy Dench's status as a highly-respected actor and a 'national treasure' than the demands of plot and Bond tradition, the role doesn't necessarily seem so different from M's role in, say, Thunderball, in which M monitors events from a situation room throughout the film. We can also note that Daniel Craig wasn't the first Bond to visit M's home. The difference between the more recent films and their antecedents is the rise of technology (at least the sort of technology imagined by the film-makers) to rapidly analyse events and maintain communication with Bond and other agents. With such technology available, one would surely expect any modern M, whoever plays the character, to have an active presence for the duration of a mission. Necessary, too, given the increasing political oversight and scrutiny intelligence services now face, a reality reflected by the number of committee meetings and ministerial meetings Judy Dench's M attends (although oversight has been hinted at in earlier films, with such statements as “No. 10's making ugly noises about Operation Bedlam”).
Returning to the Connery and Moore eras, an explanation for the uniformity of M's appearances for most of the 1970s and 1980s, which contrasts with the more diverse nature of M's role in the 1960s, might lie in the fact that the stories depicted in Roger Moore's films rely more on original scenarios and less on the pages of Ian Fleming. This perhaps makes it more likely that particular elements or memes of one film, such as those which best show the amusing interplay between Bond and authority figures, would be repeated in the next film and given some variation. As certain scenes are repeated, they become more familiar and begin to define a new or revised formula until audiences and film-makers expect them as part of the Bond experience. Returning to Fleming in Connery's films, combined with fresh story elements, or introducing an original story for You Only Live Twice, the structure of M's scenes was less stable and was effectively re-set for each film.
There are two other points worth making. The first is that M isn't the only character to have had increased screen time during the course of the series. To an extent, Q has also become more prominent (compare the character's screen time in, say, Octopussy, with From Russia With Love or Thunderball). Again this is a product of familiarity, as characters gradually become so well established within the James Bond's team, that their contributions are expected and welcomed. Finally, as I scanned through the Bond series, I noticed how the clothes style of Bernard Lee's M had changed. For all films from Dr No to On Her Majesty's Secret Service, he wears a bow tie and a suit. Thereafter, until Moonraker, he wears a tie and blazer (at least most of the time). The choice of bow tie is probably not significant, but I wondered whether it was a nod to Ian Fleming, who preferred to wear the item. Perhaps it seemed fitting to the producers and director of Dr No to include something of Fleming in the character of James Bond's chief.
This brief analysis has, I hope, highlighted some trends in the evolving role of M in the Bond films and suggested that the role of M as played by Judy Dench retains elements of the M of her predecessors, and is perhaps not so radical a depiction as might first be thought. And where there is difference, the realities of a changing world are likely to influence the role of M, just as much the whims of the film-makers, if not more so. What of the future? Mallory's introduction as M suggested a return to the traditions of the early Bond films, as his office deliberately recalled the Bernard Lee era. Perhaps, then, we can expect something of a traditional portrayal too. I wouldn't be too certain of that. While I predict that Mallory won't be seen so often in the field, and we may see more briefings taking place in M's office, the depiction of smart technology will make it inevitable that M will be shown to have the same high level of contact with James Bond as his predecessor had, enabling him to follow Bond's mission as events unfold.