The risk of injury during vaginal rejuvenation depends on what areas are being operated
Most vaginal rejuvenation surgeries are performed on the posterior wall of the vagina. The risk of injury on that anatomy is to the rectal wall which lies underneath. If the procedure includes surgery on the anterior vaginal wall, then there would be a risk of bladder injury. The risk of injury to either of these organs is very low in expert hands, but is increased by heavy scarring, weak native tissue, radiation, disease and mesh prosthetics. An expert would be able to manage these injuries at the time of your surgery.
Not Much, but Not Zero
In a "cosmetic" vaginal rejuvenation procedure, there really should be NO risk of bladder injury, because the incisions and surgery occur on the opposite side (adjacent to the rectum) of the vaginal canal and perineal body (the space between the vagina and the anus). There is a higher chance of injury to the anus or rectum, but even that risk is extremely low for any surgeon with experience operating in this area. We can never say the risk is absolutely zero, however, because if you can imagine it, it's probably happened. Most (99.9%) of these surgeries are safe and result in no long-term injury to any adjacent structures, especially in the hands of a skilled and experienced surgeon. If you are considering this surgery, do your homework, ask questions, and satisfy yourself that the surgeon you are considering does have the appropriate experience and training for you to place your trust in him or her.
I the vaginal rejuvenation includes repair of a fallen bladder, i.e. cystocele, or a bladder support surgery, there is always a possibility that the bladder could get injured.
The level of risk depends on the exact procedure being performed and the level of expertise of the surgeon. For purely cosmetic cases, the surgery is primarily on the exterior and should pose no risk to the bladder. However, this is something you should discuss in detail with your surgeon during your consultation, as they will know the exact procedures being performed and the risks associated. Good luck!