Congratulations! Just keep them watered but not soaking wet and they should do fine. When they get two or three sets of leaves you can very carefully transplant them into separate small pots and start to move them out into full sun. Don't put them into too big of a pot too soon. That seems to slow them down. You can also give them a little diluted fertilizer, like half strength, once you pot them up. Be sure to post some pictures when they bloom!

Seil, thanks! They'll have to be transplanted for sure, the container they're in is too shallow. At what age do they usually start blooming? I can't wait!

It depends on the rose. I've had some of my seedlings bloom in about 8 to 10 weeks from germination. Some others took as long as 2 years before they bloomed but those are usually from once blooming roses. Party Girl is a repeating mini and you should get blooms fairly quickly on them.