I think it depends on whether you're paying for the hot water!
If not, you could run one big hot bath each time for every client, for him to use before and after. If he's a normal nice guy with no hygiene issues you could also pop yourself in after each booking as well (before running a new hot bath for the next one).
It is more luxurious, and I think offers a better clean for clients as they are submerged!!
I think you could make the bath a selling point rather than buying a plastic shower attachment. Although you could maybe get one and keep it in the cupboard for any clients that absolutely insist maybe?