My little one also likes to come out of the support one she’s 3 months but she’s trying to sit herself up and can’t quite get there so ends up sliding off it. You can get bath seats that have straps
We had a period of about 3 weeks where we had the same before he could sit up. I put a towel on the bottom of the bath and made it super shallow. He then laid on the towel. He did roll a few times but it was shallow enough not to cause problems. Only downside is bath times had to be super quick so he didn't get cold.
I don't use that particular bath we have a lay down bath and just keep the water at the max line as my baby also likes a good splash in the bath, he does sometimes push himself off of the seat part in his small lay down bath but because we bath him on table top in his bath it's easy enough to grab him quite quick. I also find putting baby in the bath with me is a good way for him to be able to splash about and push himself about, i sit at the very top of the bath and lay him in front of me obviously holding him and he can fling his arms and legs around as much as he wants and also let him lay on his tummy while i hold his head up above the water and he absolutely LOVES this, it was the only way i felt comfortable bathing him until he was like 3 months old as i knew i had a good grip of him and there was no risk of him slipping down the bath into the water or pushing himself off anything 🤣x
This is a tough one. All you can do is say no. Have you tried a lay down bath where the water isn't deep enough if he turns his head? We bathed my little girl like this and just kept the bath short and sweet. X