i have some bath toys like these bath bobbers by munchkin
We didn't have much of an issue other than when the water was chilly. Even now he hates when the bath water gets lukewarm. We also had an incident where the shower head sprayed him with cold water in the middle of a bath when the tub switch got moved just enough to divert the water. Screaming and crying, bath time was over and for the next 2-3x afterwards he stared at the showerhead in fear. Now he loves the showerhead and wants to touch it the whole time.
Around 6-8 weeks we began introducing floating toys that the kid liked to kick as he reclined in the tub. He would kick so much he'd start to slide sideways and move the tub around! The ones we used are below, only $7 and he continues to use them in or out of the tub.
Munchkin Bath Bobbers Toy https://www.amazon.com/dp/B01G1JQY2G/ref=cm_sw_r_apan_glt_fabc_4GT16E67Y5XMFAH9E8H9
I also took baths with him in the big tub. Partner brought baby and I nursed then bathed him. Handed him back to dada to get dressed and put to bed while I soaked a bit more and showered in peace. It ended up being a good routine until he was ready to take a shower with us.
mine is a bath toy you can see it here