I saw at least some of this movie on television somewhere around 1980 (give or take a couple of years). My personal guess, in hindsight, is that the movie was probably made in the 1960s. English language; main characters had American accents; presumably produced in the USA.
The movie was a comedy, or at least had some very funny moments, but the plot was a cloak-and-dagger type of thing -- nasty foreign spies as the heavies, I think. The co-stars were a young man in a conservative business suit (I don't remember if he worked for a government agency), and a young lady who surprised him by turning out to be a gifted martial artist. (I'm thinking "judo" or something similar -- as in, throwing big men around when they tried to grab her.) I believe she was blond. (But I was watching this on a black-and-white TV, so I can't swear to it.)
I remember one sequence fairly well. It must have been toward the middle of the movie (I think I'd come in late, and missed the first bit, but I'd seen a few scenes before this part happened). Here's how the sequence went:
The leading man, the leading lady, and possibly some other people, are all staying in the same house. The girl is taking a bath -- specifically a bubble bath, so that when the camera shows the interior of the bathroom to us, we don't see too much of her. Just her head and at least one arm poking out from a huge mound of bubbles inside the bathtub, which completely conceals all the rest of her body.
At least one bad guy gets into the house, somehow. I think his goal was to kill the girl, but it may have been something else.
We see the bad guy go quietly into the bathroom where the heroine is having her bubble bath. He sneaks up behind her, so that she doesn't immediately realize she has company. Then we cut away to see what the leading man is doing.
Somehow, the leading man becomes aware that there must be an enemy agent inside the house. (Perhaps he found an unconscious sentry, or some other evidence of recent intrusion? I can't remember what, but he knows he has a problem.) He comes running down a corridor in search of the intruder -- sees the open bathroom door -- and suddenly relaxes and steps back, possibly leaning against a wall and folding his arms, as a way of silently telling the audience that he is not the least bit worried about the heroine's ability to take care of herself; he just wants to stay well away from the doorway until the fuss is over!
About two seconds later, his confidence is justified. There's some noise from inside the bathroom, and then the bad guy comes flying out the door (and probably, though I'm not sure, collides hard with the wall on the far side of the corridor). The implication is that the girl realized she had company, stood up, and used a judo throw or something to expel the intruder. Which, of course, we didn't get to see, because this wasn't the type of movie that would have nude scenes.
If I saw any more of the plot after that, I don't remember it now. I've never run across that movie again. Can anyone help?
Addendum: The Candidates that I've Ruled Out!
After looking at the comments I've been getting in the first 22 hours or so, I'm going to list some of the movies which I have seen recently enough for me to be confident that they are not the one I'm now seeking.
- Our Man Flint (1966).
- In Like Flint (1967).
Both starred James Coburn as Derek Flint. I've seen both within the last 10 years.
- The Silencers (1966).
- The Ambushers (1967).
These were two of the Matt Helm movies made in the 1960s with Dean Martin as the hero. Wikipedia tells me there were four in the series. I had seen The Ambushers before I posted the query, and I have now (12-14-2016) seen The Silencers as well. Those two definitely are not the one I'm asking about, and I strongly suspect that neither of the other two would qualify as the right answer, either. I don't think the leading man in my movie looked anything like Dean Martin, nor was he supposed to be as charming and as much as "a man of action" (nor such a womanizer) as the movie version of Matt Helm is supposed to be.
- The Nude Bomb (1980), aka The Return of Maxwell Smart, aka Maxwell Smart and the Nude Bomb.
I saw this one several years ago, and it wasn't the one I described above. Other movies (and a later TV series) based on the original TV show Get Smart all came out long after the timeframe (circa 1980, give or take a bit) in which I vaguely remember seeing the movie I'm asking about in this post.
Dr. Goldfoot and the Bikini Machine (1965).
Dr. Goldfoot and the Girl Bombs (1966).
I own both of those Vincent Price comedies on DVD, and they do not contain the sequence I described above. (Nobody had nominated them yet, but I decided I might as well eliminate them right now, in case anybody was trying to remember if there was a scene with one of Dr. Goldfoot's beautiful robot girls taking a bubble bath and dealing harshly with an intruder.)
- Carry On Spying (1964)
As I type this note (on 4/28/2017), I've recently watched this film. It has a beautiful blond girl who's just been trained as a spy as we first meet her, but she doesn't demonstrate any expertise in hand-to-hand combat in the course of the film, nor does an assassin interrupt her while she's taking a bath.
Second Addendum: Not One of These TV Shows! (added 1/16/2017)
I have said all along, beginning in the opening sentence of the original post, that I was looking for a movie. As in: a full-length feature-film, with a self-contained story about characters who were only created for that single script. I'm sure it wasn't just a formulaic episode featuring a male/female pair of secret agents on their latest weekly assignment. Nonetheless, I have seen suggestions for one old show or another. I've replied in comments to those suggestions, but, for the benefit of those who don't bother to read the accumulated comments before answering a question, I've decided to address the matter here.
It could not have been an episode of The Avengers (1961-1969). I've seen every episode which had John Steed working with a female partner. (I have most of them on videotape, and some on DVD.)
It could not have been an episode of The New Avengers (1976-1977). I have all those on DVD.
It could not have been an episode of Get Smart (1965-1970). I have all five seasons on DVD.
To reiterate: I feel certain it was not an episode of any other old TV series with a cloak-and-dagger theme, either, but I can swear from personal observation that it was none of the above.