J.,
I used a bath seat with all four of my children. The suction cups will stay down pretty well if you don't have a textured bottom on your tub. If you have the textured, "no slip" bottom on your tub, the suction cups will occasionally pop up which can make the seat tip over.
I always bathed my two littlest ones together. I made sure their diapers, towels and PJs were right there in the bathroom so I never had to leave or even turn around when I took them out one at at time. If you are worried about where one will go when you are getting the other one out, set up the bouncy seat or pack and play right outside the bathroom door (or inside if it fits.)
If your girls are 9 months, they are plenty old enough to sit in the bath with bath seats. In fact, when they are somewhere between 9-12 months old and can sit up in the bathtub without slipping and falling over, you don't even need a bathseat. You can just set them in the tub with the water filled up to almost cover their legs.
I know that there is a TON of scary information about child saftety in the bathtubs. Please understand they are talking to the moms who leave the bathroom to go answer the phone, watch TV, check on dinner, answer the door, etc. If you are in the bathroom with them the whole time and attentive, your babies aren't going to drown. Even if they did accidentally tip over with or without a bath seat, you are right there to grab them.
All four of my kids tipped over once or twice. Sometimes they got their face wet. It was unpleasant and they learned to be more careful, but no one ever got hurt because I was always right there to grab them.
Good luck,
S.