My dog is bleeding, vomiting, and hiding under the bed. What to do?

This is a highly unusual situation, and in my 10 years of being a vet I have never heard of a male dog attempting to have sex with a spayed female dog. However, what is most important now is getting Lucille out from under the bed and getting the bleeding stopped. I would suggest gently nudging her out from under the bed with the long handle of a broom (using a sweeping motion and not poking her with it) or consider dismantling the bed and removing it in order to gain access to her. Once you have her, place a lead around her neck so that she cannot hide again. You will need to apply direct pressure to the vaginal area in order to stem the bleeding. Hopefully no arteries were torn and the bleeding is not as profuse as you think it is. Once you have pressure on the wound you will need to again try to reach the vet in your area. She may have tearing that needs to be addressed ASAP in order to prevent infection and further blood loss. Adding ice to your compress may provide some constriction of the vessels and slow bleeding until you can reach veterinary care.