When we brought my father home with hospice, we moved his bedroom down to the main floor of the house. The main floor bath has a claw foot tub with a shower attachment. We made a 'bench' from treated lumber that would fit securely over the tub, with boards under the bench portion on either side to hold it in place; then we padded the board and made a cover for it from a heavy duty plastic shower curtain. He could either sit on the bench to wash up, or push it forward, sit on the back 'lip' of the tub and slide down into the water and also as a brace to get out of the tub. We resurrected/recovered the bench when I had tibial plateau fractures and again when I had knee surgeries since going up and down stairs was painful. It was heavier/sturdier than the plastic bath bench the Legion offered us.
We use rolling shower chairs at the hospital and I can't tell you how many times we've had issues with slips/near falls. Unless the wheels on the chairs can be locked down, they are a menace. The regular shower chairs are somewhat flimsy as well, unless you are able to find a high quality, heavy duty one - most of the ones I see aren't heavy enough. They do have ones that have a sliding seat - you sit on the seat and it then slides over to get you into the shower/bath. It works a lot better in a shower than a tub.