This is an older movie, likely pre-1970s. A lifelong bachelor is determined to never get married, but his long time mistress wants him to propose. He doesn’t understand the point of marriage, so she decides to make him jealous by pretending to have another suitor. He eventually becomes jealous, there are some misunderstandings with him thinking more is going on with this other man than really is. In the end he decides to marry her.
How to Save a Marriage and Ruin Your Life (1968)? https://www.imdb.com/title/tt0063102/
Unfortunately no, though I now see that my description describes that movie too! The woman in the movie I’m thinking of is the man’s long-term girlfriend/mistress at the time of the film, and he wants to continue their relationship unmarried.
I know you said he’s a bachelor and in this movie the plot matches a bit (he’s married but has womanizing ways) so I’m suggesting it anyways!: No More Ladie (1935) https://en.wikipedia.org/wiki/No_More_Ladies. Sometimes our memories of something can be foggy, how long ago did you see it?
Also, do you remember some dialogue from the movie? https://www.quodb.com/search could help you!
Or this one: Fräulein Casanova (1953) https://www.imdb.com/title/tt0044641/?ref_=adv_li_tt. Wikipedia has more plot info, but this one’s only in German (but adding the link in case you know German! https://de.wikipedia.org/wiki/Frulein_Casanova). This plot also is smiliar to what you’re describing.
“Every Girl Should Be Married” (1948)?:
https://en.wikipedia.org/wiki/Every_Girl_Should_Be_Married