If its not the exercising that's causing the bruising, I guess its plausible that exercising might make you more prone to it. Bruising is caused by blood rushing to the surface of injured skin to repair it (or something like that), and regular exersize will improve your hearts condition and slightly elevate your blood pressure if you have low pressure to start (and lowers it if you have high pressure).
I know for me, I have always had really low blood pressure (I used to faint a lot when I was a teenager, and I also can't maintain my own body temperature very well), and since I've started doing cardio exersizes I've been getting dizzy a lot less often and also can keep myself warmer in cooler rooms.
I'm not very good with biology though, so I wouldn't take any of what I said as gospel, but it makes sense to me.