R.D.
Time for a second opinion!
If you don't floss regularly, then go to the dentist and they floss for you, yes, it could be nothing; just the trauma of finally flossing.
BUT... it's more often than not a sign of gingivitis or... I forget the second, very common, very managable, very preventable dental condition.
Just brush and floss regularly, and you should see a huge decrease in the amount of bleeding. If you have any other side effects like a white, fuzzy tongue, or bad breath no matter what... get a second opinion.