Couple of things - when you bought your hyacinth bulb, was it a prepared, pre treated one, sold specially for growing indoors? Or was it just an ordinary outdoor one? It's usual to buy a prepared one for indoor growing, to ensure they flower in late winter rather than waiting for late spring, as they naturally do, so the fact yours has already finished flowering probably indicates it was a prepared bulb. As such, it will not perform in the same way this coming winter, and won't flower till late spring, so the best thing to do with it now is to plant it outdoors and let it revert to its natural growth habit.
I'd just add that, while the foliage is present, that is the time to feed the bulb, so that it can store enough energy to create a good flower for next year. If you have space outdoors to plant it, and it's cold where you are now, take the opportunity to add some fertilizer when you water, while it's still got leaves, then transfer it outdoors after hardening off (see What is 'Hardening Off'?)