Hello,
Hymen is a thin membrane covering vaginal opening externally. It varies in shape and elasticity in different females. It can be torn with slightest of injuries due to exercising, Gynecologist examination, bicycle riding , masturbation or other accidental injuries. In other cases when it is very elastic, hymen can retain to its normal position even after child birth. Remnants of hymen membrane (carunculae myrtiformis) can be seen through vaginal examination when it is torn or lacerated by any reason. But, there is practically no way to tell specifically the reason behind a torn hymen in a given female.
In your case, it is difficult to say that finger penetration has caused hymen to break or not. This can be confirmed only by vagina examination. Although tearing of hymen can cause mild often insignificant bleeding, in your case it can be due to injury to the vaginal wall mucosa as finger nails can often scratch the sensitive lining of vagina. If bleeding is more in volume it can be due to menstruation if you are near your dates. In any case there is no reason for worry. Clean the vaginal area well with warm water and mild antiseptic lotion or soap. If the bleeding does not stop and you are not sure if it is menstrual bleeding, then visit your Gynecologist for further examination.
Thank you. Hope this helps.