I think it's even better to pay the bands a little less, and allow them to pass a basket.
I just hate having to panhandle at an establishment I'm performing at. It comes off as desperate, makes the establishment look like they're cheap and underpay their entertainment (obviously they are) and makes me feel like a second class citizens begging for change. If you can't afford five dollars to see a band, stay home. If you can't afford to hire a band, don't hire one. Try paying for toilet paper with "exposure". You'll wish you could afford soap.
I also don't think there's any science to this at all. If I owned a bar - what I'd most likely do is try everything for a while to find out what worked best.
The problem with that idea is that there ends up being no consistency. We've all seen the bar that struggles to find its identity and tries everything, only to alienate all of its potential customers in the process.