You’d have to ask a plumber as it would be very specific to the build of your house. My understanding is that grey bath and black toilet water eventually go into the same drain so you would have to divert the waste bath water.
There would need to be a switching mechanism to re-divert the bath (or over-bath shower) water into the drain once the butt was full, which it soon would be if you are not using the water in the garden every day, else the butt will soon be overflowing.
An average bath uses around 80 litres of water. A small butt only holds 100 to 150 litres. A medium one 200 to 250 litres.
It costs around 35p-40p for 80 litres of metered water including sewage charges.
Also, what would be the situation with the chemicals in bath, shower and hair products as well as the general grime, skin and hair loss that goes into the water system?
I think this a question best suited to the Screwfix Community board for the technical aspects of installation and use.