You are on the right track, but as someone has commented your conjugations need some work.
However, I'll give you what I would suggest is a natural way to ask this.
ドラムを叩き始めてどれくらいになりますか?
I think you could replace 叩き始めて with simply 叩いて, but I think the above is more clear.
Besides your issues with です and ます, you don't need to use 貴方. Often in Japanese it's best not to use any word for "you", as it is implied and each word that means "you" has its own nuance.
If you want to use this for other things, you can just put the action in the "pre-masu" form (i.e. 食べ) followed by this phrase:
〜始めてどれくらいになりますか?
This would translate to "How long have you been ~?"
EDIT: Replaced 〜ですか with になりますか
EDIT: Added general pattern