"Yes? I am sorry!"
"bocsánat" or "bocsáss meg" means "forgive me"; "sajnálom" means "I am sorry"; "elnézést" means "excuse me"
Very simplified: elnézést = excuse me. bocsánat = when you did something wrong and you're sorry about it. sajnálom = when something bad happened to someone but you didn't have anything to do with it.
In this very context elnézést and bocsánat are pretty interchangable. Sajnálom also means something similar but I wouldn't use it here.
It is more like a question of style. I see nothing bad in using "sajnálom" here (and I am native Hungarian living in Hungary).
about 'bocsi': besides of being very very informal, it is kinda stupid using diminutive where it is not absolutely necessary. think of a counterfeit LV handbag and a genuine duckface selfie.
Counterfeit LV handbag and duckface selfies go better with "bocsika" which is an even more diminutive and more stupid form.
I don't think so: "bocsi" is very informal. You can use it with people whom you can lightheartedly can say "thankies!"
Um, I say bocsi to everyone when I'm in Budapest and bump into someone in a shop for instance. :D