[The Happy Squirrel]

First I must say I've never drilled a barrel (yet), with that said....

You may be OK with a regular length bit, but a shorter one would be stiffer and less likely to wander.

If you are worried about the drill bit wandering when starting on the barrel a centering bit would probably help out.

http://www.bing.com/images/search?q...D174475B58CD562FE26B9D8EA9EC5&selectedIndex=7

These are used to start the hole but not drill all the way through. Get a bit that will just fit through the hole of the receiver with out enlarging it.
If you have a bench grinder you can make a transfer punch from an old drill bit that fits snugly into the receiver hole. This will ensure your actually starting your hole centered in the receiver hole.

http://www.bing.com/images/search?q...A2032E5877395F4EFAAC4D374E0B7&selectedIndex=1

http://www.bing.com/images/search?q...C189D6F91AA37C232E97276F1B6FC&selectedIndex=8

I think I read on here somewhere that people have cut a slot into the barrel instead of drilling. You may want to search around for that method also.