Yes it is perfectly normal! When a dog is in head they do bleed rather a lot. Its very messy! A swollen vulva and bleeding are juts symptoms of heat. If you don't want to deal with her just get her 'fixed' by a vet or get doggy diapers. And if you don't want to breed her keep her enclosed and away from males for sometime.
Ah, lil girlie dogs. They can do weird things. My lil girl slept in the bath tub! She hates taking baths in there, but she slept and napped in there. I am at home and have never left her in there with the door closed. Her first cycle also brought on the hiding treats and bones. She will bury them in her bed, under blankets..we kept finding them in odd places. Come to think...I do some odd things myself ;)