Rinsing the new gravel in tap water will not harm your existing bacteria colonies.
You could also do this.......go buy a very cheap plastic (tupperware) type contanier. Square, round it does not matter. You should be able to get this at any dollar store!!
Make sure it is food grade safe. Rinse it out with just tap water. After you have cleaned the new gravel, then simply fill this container with it, place it slowly in the tank, let it sink to the bottom and dump it!!
There simply is no need to move your fish to accomplish what you want to do. After placing each container of new gravel in the tank, thne gently mix it in with the exsisting gravel.
I move gravel around all the time and believe me, even when I dump it from just below the water surface the fish scatter very quickly!!
CM