I bought Tulips and Daffodils at the store. I want to know after the flowers die off can I plant the bulbs, or do I need to wait for a certain time of year?

welcome to GoY.
Plant your bulbs as soon as you want. they will be fine. the foliage will die back and then they go into a dormant state until it is time to grow again.

Yep agree with Seaburngirl, i have some in a display that was a gift when its finished i will put them in the garden, one is a Hyacinth and the other are tete a tete daffs, plus a primula

As soon as any of my bulbs start to fade. I plant them in the garden. pull there heads off once they have finished flowering, (stops energy going into seed production). Give them a liquid feed later on in the year and they will return in abundance next year.