I asked for a recommendation, then decided I wouldn't, but I've changed my mind again. Will the professor feel annoyed? I was planning to apply for a Ph.D. program and I asked a Prof to write me a letter of recommendation. The prof already agreed. After that, I didn't feel confident about applying and informed the professor to not write LOR for me. 

Deep inside, I still want to apply but I haven't made up my mind yet.
Will the professor feel annoyed if I ask for a LOR again? Should I tell the professor that I haven't decided yet but in any case, can they still submit their LOR.

I know professors are busy and I don't want to bother them too much.
Probably yes. 

Writing a strong letter of recommendation demands some effort. Make sure of your decision before asking for your professor to invest his time in it.