Gee, you must have a lot of disposable income if you're thinking you just pay whoever you think you might photograph on the street.

Just do it. Do it respectfully, the advice given above by lensworker is close to my experience. Sometimes I say and ask outright, other times I do it discreetly. At any time, I'm not out to 'cheat' someone or pull a fast one.
I'm in the midst of getting a business card printed up for my upcoming website and the street photography blog I've started (reservedatalltimes.com) so if anyone asks or challenges me, I can just hand out a card with the website and explain it calmly...honestly, it's never been an issue.

Stop worrying, start shooting. Experience is your best teacher.