I cannot speak with medical experience, nor theoretical referenced material to back up my opinions on bruises - only my personal experience. That said here's what I've figured out for myself.
I was very low on iron. Not anaemic, I was low in ferritin (had no idea until I had a blood test tho) - so it wasn't showing up as the regular anemia - however my symptoms were exactly the same. I ended up having to have 2 iron infusions - not fun! But it helped my energy level significantly. I was sooooooo tired before, didn't have energy for anything - even fun stuff.
Anyway, I noticed a pattern. When I was low in iron (ferritin) I bruised very easily. I got better shortly after the first infusion and then as time progressed and my iron levels got low again (altho I didn't know yet until I had another blood test) I was bruising alot again and thought to myself that it was likely I was low in iron again.
I researched natural iron supplements cos I didn't like the idea of continual iron infusion (the Dr told me that the norm is perhaps once for a person, or once per year if they have chronic iron problems, so two iron infusions in the space of about 6 months was not cool in my books!) Anyway I found out about Spirulina. I only take the tablet form at this stage cos I couldn't stomach the powder (but there's others here who do the powdered spirulina) It's mega rich in iron - sorry don't have stats. But has helped me tremendously.
Hope your Dr can help.
Let us know how it goes.
PS. I do understand how embarassing it can be with the bruises - I didn't do any martial arts of any kind, but understand from my friend how easily you can bruise with that. I just had bruises from knocks and such - or friends grabbing my arm too excitedly to tell me stuff etc, people used to think I was being abused - not good.