Part of the ceremony in Grave Peril was Bianca becoming a Red Court Noble. This was not only a ceremonial thing, but an actual supernatural event. Before then, Bianca did not have the ability to create other vampires. So, not all Red Court vampires can create baby vampires. I think that to create a new vampire you have to be a noble, keep them alive, and do something special/different when you feed.
In the books, especially Changes there is talk about the Red Court valuing those who can control their hunger and are not controlled by it. Part of the reason there was a power play in the Red Court was because the Red King was losing control of himself.
A quick note about BCV:
In It's my Birthday Too - one of the short stories - there is a Master BCV who's been a BCV for maybe a year who makes minions during the course of the story. As in the entire struggle doesn't take more than an 1 or so and she makes and deploys 3 minions - which means they didn't need to rise.
Also, Tomas has fought other vampires and has no problems with the minions, but can't beat the Master because it's a master.
Richard