I use a thin shower cap - like the kind you get free in motels/hotels to cover my hair when I apply colored shampoo to tint it. (Got that from a hairdresser who did that and put me under the dryer.) I just sit in a hot bath tub for 10-15 minutes. Seems to work.
I just use a plain old plastic grocery bag for that. I use the handles as little ties. No one sees me dye my hair, I don't care what it looks like. It seems to keep the heat in, which helps the colour stay, and it's no big deal to throw it away when you're finished.