I'm sorry to bother you. Can you change it to I'm sorry to bother you? Why should we add "have" after "sorry" ...

You should analyze the composition of this sentence in order to understand the grammatical phenomena inside.

I is the subject, am is the copulative verb, sorry is the predicative, and the whole sentence is the main system table structure.

Excuse me is a supplementary explanation of sorry, that is, "I'm sorry for what", which is grammatically called slogan complement.

The reason why we use the perfect infinitive, that is, "to have done", is because what we do is before "sorry".

I hope my explanation will make you understand.

You can ask questions again.