That would be a little bit "overly polite". "Allow me" and "apologise" in the same sentence is a bit too much if you think about it... But technically there is nothing wrong with the sentence.
"taking up your time" would be another option.

It depends on what you are going to use it for. Mail shots (commercial mail) usually starts with phrases like that. Personally I stop reading at that point! Spam emails and the like too, and surveys.

If I was talking to someone I know, I'd just say "Sorry to be taking up your time with this, but I really have to ask your help... I don't know anyone other than you who can____________. Can you spare a minute?"