usual method is to take the Method bathroom spray (which is pretty environmentally friendly, I think, since the main ingredient is just citric acid)

This. I have a similar eco-cleaning spray that's basically citric acid. As and when the bathtub's looking at all grimy, I spray it with that, rinse it with hot water from the shower attachment, and if any areas are left looking manky (e.g. if I've been using oils in the bath, as they tend to cling to the walls), wipe them down with a micro-fibre cloth. Very speedy, and any citric acid residue isn't going to hurt me.