This really depends on the bar. Sometimes you'll get lucky and despite the fact that you're at an after-hours bar in Kinshicho, the staff is fully fluent in English and you have no problems whatsoever. However as a rule of thumb, the more famous a bar is, the higher chance you have that they're used to dealing with non-Japanese speakers. Of course hotel bars are by far the safest bet here, but if you are just going to drink at your hotel, you probably wouldn't have come to this site. Right?
Even if you speak no Japanese at all, don't worry. Hop on over to the Japanese Bar Phrasebook and start gettin' your Japanese on.