Unexplained bruises on legs but normal blood count?

Possible yes: Blood count offers limited information. Even with normal platelets you can have coagulation disorders. I would suggest to go and get evaluated by a physician to make sure no further work-up is needed.

Bruising: Easy bruising commonly can be caused by different factors including- low platelet level / abnormal function of the platelet, blood vessels abnormality, or abnormal level/function of coagulation factors . Many things like drugs, endocrine problem, trauma, acquired/congenital condition can cause above problem. You should discuss with your md. If it is complicated, you should see a hematologist.