After the bath soaps have been used, tiny bits remain. Note that this is not about re-using half-used or little-used soaps such as found in hotels. I am aware there are charities such as Sundara Fund that upcycle them. I want to know what can be done with tiny lefover bits.
I'm not sure about donating leftover bits... But for recycling/reusing, what I normally do is grab a new bar, and at the end of my shower/bath, get both the new bar and the small used piece(s) wet and squeeze them together relatively firmly. Leave it in the soap dish / on the shelf and they will dry that way. The next time you shower/bathe, you'll have a slightly larger bar of soap, and you won't have wasted any of the old soap!
Another option would be to use a cheese grater to turn the soap into flakes for use as laundry soap. Lux, in fact, is available as laundry flakes from the supermarket. Cannot comment on the biodegradability of Mysore Sandal, however the MSDS for Lux claims the product is biodegradable. Unfortunately no information on eco-toxicity.