Bathsheba's love affair with Frank, although in its infancy, could easily have lead to rumours being spread around the town of Weatherbury, thereby threatening her livelihood within the community. In addition to this, Boldwood has become enraged with jealousy and Bathsheba fears he will turn violent towards Frank, should the inevitable confrontation occur. So despite being in love with him, or perhaps to protect him, Bathsheba sadly laments to Liddy that Frank must be given no encouragement in coming to Weatherbury. (In the novel she even goes so far as inhabiting a distant town to discourage his presence)
The film may well have depicted their timeline with added fluency because, as you have pointed out, Bathsheba appears to have jumped from one resolution to another almost on a whim. This does make the clandestine meeting on the beach seem a little abrupt, but perhaps this was intentional and only momentarily misleading; all in preparation of Frank's bombshell to Boldwood which is to follow.
As for Boldwood's resort to bribery: it was a desperate measure; unmanly and dishonourable, and most unbecoming of the otherwise noble squire. Rejected, he pleads with Frank to take the money regardless of his intentions towards Bathsheba, in the forlorn hope that he can somehow yet be inveigled to his immoral and corruptive scheme. Boldwood's unenviable and unnecessary humiliation becomes all the more exacerbated, and to him unbearable, when he realizes Bathsheba & Frank are by now already Man & Wife.
Thank you Neverj. That was very informative.
Rejected, he pleads with Frank to take the money regardless of his intentions towards Bathsheba, in the forlorn hope that he can somehow yet be inveigled to his immoral and corruptive scheme.
No. His switch to "bribing" Troy to marry Bathsheba was motivated by Victorian propriety. He assumed that they were about to be intimate (or already had been), and did not want Bathsheba to be ruined by Troy's failure to marry her, as had happened with Fanny Robin.
His love for Bathsheba was protective, even proprietorial, rather than physical, as is shown by his words and actions throughout.