I think it is definitely possible to reuse bath water in a small terraced garden, but I would keep the system as simple as possible. Rather than installing a large water butt, I would use a compact container or a simple siphon pump to transfer cooled bath water directly to the garden when needed.
The main advantage is that it reduces water waste and can help keep the garden watered during dry spells. It should also be relatively inexpensive and easy to manage without taking up too much space. However, I would be careful about storing bath water for long periods, as it can develop unpleasant smells and bacterial growth. Ideally, it should be used within 24 hours, applied directly to the soil, and kept away from vegetables and other edible crops.
I would also use mild, plant-friendly soaps and avoid water containing bleach or strong cleaning products. As for water bills, the savings would depend on how much water is reused and whether the property has a water meter. The financial benefit might be modest, but the environmental benefit is worthwhile.
My preferred solution would be a small, discreet system that can be removed easily if necessary. That would make it practical for a small garden without creating a permanent feature that might put off future buyers. Overall, I would try a simple, low-cost approach first rather than investing in a complicated installation.