Our first child showered with us at about 3 months perhaps, but our second started about 2 weeks! It's so much easier! Especially if you have someone to help you.

I'll hop in the shower, and dh will undress bub and bring him to me. It's a careful handover, but then I have him upright looking over my shoulder (get my hair out of the way or he pulls it), and then let the water fall on his back. I'll wash him in that position. He likes it quite warm too, so I'm still comfy. I just don't use any soap really on him, don't want to make him slippery!

And then when I'm done, I just hand him back to dh to be dried and dressed! It's so easy, and he really likes it. I just chat to him when the water first hits his back, or put my hand on his back and then move it - initally the water can startle him.

Something else I do - do you have one of those shower attachments you put on your bath nozzle? I put a bathmat/handtowel on the bath floor, get the warm water running, and put bub on the mat in the bath. I put a facewasher on his chest and wet it (to help keep him warm), and wash him that way, just running the water over his body. He tries to hit the water and hold it, it's pretty cute. :P
But there's no danger of him slipping out of my hand that way. I wash him that way when I'm on my own.