What is the best way to approach a bar regarding late night DJ entertainment? I would like to find a night gig one or two nights a week. I can send out postcards or visit the bar in person. What has worked for you?

Many of the bar managers I've worked for were not oriented to spend much time with resumes unsolicited letters, post cards or promotional materials. The face-to-face thing is your best bet. I would call ahead to be sure the manager would be there and I tried to be there when nobody else was there, just before noon if their hours allowed that, so I got as close to undivided attention as possible.
It did not work every time but often enough so I was working 6 nights a week when I wanted to.
What are you offering? spinning, Karaoke, something else?Paul
Spinning - Use to work at Bobby McGee's and Black Angus many years ago and all ways had a good time.
Are you planning on approaching an establishment that does not have a dj at the moment?