Without telling us what they bought there is no way to give you an answer for your situation.
That being said I have never, will never, would never screen bidders. I have never, will never, would never cancel a bid unless I stumbled across a bidder with whom I had a previous unpleasant experience.
Just this week I made a very smooth sale to a previous NPB, last time he couldn't seem to figure out how to pay, this time he paid in 2 days and bought another item off eBay.
In 25 years of traditional retail the only shoppers ever banned from the store where the shoplifters, time wasters, window shoppers, people who intentionally ask for things you don't have, people who complain about the prices, hagglers and even a few drunks.....all welcome.
Believe me you can't tell the thieves until they make an obvious move and I know I had a few customers who were no doubt ripping off Sams or HMV but they would never consider doing it to me.

"What else could I do? I had no trade so I became a peddler" - Lazarus Greenberg 1915
- answering Trolls is voluntary, my policy is not to participate.