Is is a hand operated pressure sprayer (the type with a manual pump handle and lance) or a high-power pressure washer that is mains powered?
I definitely wouldn't use bleach in a mains powered pressure washer, but I'd happily use it in a cheap pump sprayer (and have done so before). I would be very careful about using bleach to clean your patio, as it could make it worse depending on the stone - if you do use it, be sure to dilute it! We have a sandstone patio that was covered in black spots and we had a lot of success with some "green away" product a few years ago (cost about £8 and diluted 3:1). Just be sure to do a test patch. It did take a few months for the black spots to fade.
Colin's method of using vinegar looks like a really cheap and relatively gentle way of cleaning paving, so may be worth a try first!