Looking for a movie...

I'm looking for a certain movie (don't know year) that has a same plot theme but more dramatic, I think.
The only thing I really remember, is that a man courts a young woman and gets her to accept his proposal, but then she finds out it was no more then a bet.
She runs away broken hearted and the man realizes he's actually in love with her and follows her to make things right again.

Does this ring any bells? Can someone please provide a name for this movie? It's bugging me for days now and driving me nuts!