Ob-Gyn questions? Ask a gynecologist online.
If you had a pap smear at the time of the bimanual, then some amount of bleeding can occur - this is due to scraping of the pap brush across the cervix. But bleeding, if it does occur, is usually very minimal.
If the bleeding has continued and it is bright red now, chances are that you have an infection on the cervix. A small polyp ( a benign tumor) on the edge of the cervix would also cause similar bleeding. A cervical erosion can also sometimes cause this type of bleeding. Both cervical erosion and cervical polyps would have been picked up if you had a visual inspection of the cervix with a speculum at the time of the bimanual. If you had a simple bimanual xamination with only the hands, then these could have been missed.
Please consult your doctor again - you need to be seen and if necessary, an ultrasound of the uterus may be advised.