How large would you say this airship has to be?
It depends on how many patrons you wish to serve. The smallest dirigible ever could only hold one person in a cage below it, whereas the largest was designed to carry up to 90 people including passengers and crew. The funny thing is that the same wiki also mentions it carried 2,798 people in ten round trips, which would average almost 140 people per trip - must have been really tight.
What would the logistics of flying it be?
The same as for any dirigible trip, plus the logistics of a pub, plus the logistics of a brothel.
I imagine you will be picking up the patrons at an airport, and then taking them either back to the same airport or another one. Should be troublesome to exit a brothel via a one-mile drop otherwise.
Can it be flown by gas? If not, then what?
Historically these things have been flown by being filled with gases that are lighter than air. If you meant gas as in gasoline, I believe diesel is more efficient for the engines required to move dirigibles around. In any case diesel was the fuel for the Hindenburg.