I read this thread last week, and want to add my support to the "be direct" approach, several reasons:
He's doing a professional job - it wouldn't do his reputation much good if he misread signs from a customer, asked her out and she took offence - so if I were him, I'd play safe unless 100% sure.
If he says no, it just means he doesn't want to go for a drink with you. It doesn't mean you're ugly/unattractive/whatever you might fear.
Even if he says no, surely he would be flattered? I always turn this around - if someone asked me out, and I said no, would I think less of them? No, I'd think they were brave, and I'd respect them for it.
If he says no, you don't have to see him again.
If he says yes, you'll have a date to look forward to.
Two years ago, I was in a similar situation to you. I knew two different men, and quite fancied them both. So I contacted them both, and asked directly if they would like to go out for a drink/date with me. One very nicely said no thanks, and has remained very friendly whenever I've seen him since. He just didn't want to get involved with someone who had kids - fair enough. The other was really chuffed, and said he'd been plucking up the courage to ask me the same question. We're now engaged and planning a wedding.

Take the plunge!