Chelle, I also neglected to keep in mind that the flower bed would be getting much better attention than a hayfield - likely regular fertilizing, adequate watering, good sun exposure, etc. That would also only make the thistles more robust. We only mowed our thistle-thick fields maybe twice per season, mainly trying to NOT allow the thistles to set seed to break the cycle that way. When I encounter a thistle in my flower beds (now a rarity thank goodness) I try to dig out the entire plant, including all roots. That seemed to be a bit overwhelming in Ann's case, so was trying for an alternate method that didn't include herbicides or chemicals. It may well come down to old fashioned hand-weeding - and that can be nasty with the thistle thorns!
Ann, if that is the route you must take, try to break your job down to smallish 3 square foot sections and tackle one at a time, mulching heavily once you have that section cleaned out. I get a good deal of instant gratification when I can visually see progress, and am rejuvenated once I have exceeded the half way mark.
Good luck, and do post pictures as you go so we can cheer you on!