I seriously doubt this is caused by masturbation unless you are doing penetration with a dildo that is not a quality silicon rubber.
I feel any cold pressed oil like grape seed, apricot, avocado are all good to use as lubricants.
Anytime something bleeds on a regular basis other than your period indicates something is out of whack.
I always recommend using additional lubrication for all forms of penetration.
BV is a broad category that includes yeast overgrowths, the most common problem for modern vaginas due to the amount of sugar consumed.
Yes, you can get OTC remedies for this.
It sounds to me as though you might be dealing with a stubborn hymen that might be especially thick.
Continue to mop it up and to experiment.
There are many different kinds of lubrication's that enhance penetration sex.
Get on top and control the stroke.