Luna went into heat the other day

We wanted to get a little more weight on her before spaying, so now she's 10.5 months old and is having her first heat. The vet won't spay until a month has gone by, now.
She won't wear the diaper thing I bought, but she's keeping herself really clean, just a drop here and there on her bed. How long do they normally bleed?
Don't worry, I'm scheduling her spay for August, when everything is back to normal with her female stuff and our vacations.