The bulb structure contains all the food and nutrients (apart from water,) necessary for the bulb to grow, and flower. Bulbs are little power packs and do not need additional nutrients to produce flowers for the next spring.
Save and reuse compost from any end-of-season containers you are emptying, provided it is healthy compost. This should be apparent if the plants you had previously grown in it were healthy.
If you are growing Tulips and intend to treat them as annuals, which is often the case, there is no need to feed them.
In the case of the bulbs which you intend to keep for next year, use a high potash liquid feed fortnightly after flowering to encourage the bulb development for next year.
If you continue to grow the same bulbs in old compost each year, you will need to feed more and add nutrients as time goes on, but new bulbs are fine in old compost.
Melcourt Sylvagrow is excellent compost but it comes at a price when we are all trying to save money. Keep the expensive compost for the plants which really need it.
More money saving gardening tips.