Will raising prices effect the bookings that are already in place? If they do, can I still somehow keep the prices the same for the clients that are booked?

If you raise your price, it will not affect any bookings already made. The customer has already paid for them.

If you want to keep existing customers at the old, lower price, then you will have to manually adjust the booking when it is submitted to you. That's rather easy to do. Just inform those clients that, while you will be raising your rates for new clients, they will continue to receive the old rate despite what the profile states.