What kind of bulb are you referring to? It really does make a difference.

Marianne, after my potted bulbs finish blooming, I plant them in the garden. My zone is not the same as yours, so that may not be the best thing for you.

1) Paperwhites which say that they are for indoors
2) Hyacinths which say specially bred for indoors
Thanks again,
Marianne

The hyacinths were not bred for indoors, but conditioned, i.e. refrigerated, to bloom indoors. You get conflicting reports about whether they are worth replanting. Last year I put mine in the ground and I will be happy if it comes up at all. I've been warned not to expect blooms the first year as it recovers from being forced. Hopefully next year. If you do try to save it, make sure you let the foliage go brown, either in the ground or in the pot, before you pull it off. It's the foliage that feeds the bulb to provide energy for the next year's growth and blooms.

I don't know about the hardiness of Paperwhites in Chicago, although somebody here probably does, but I figure, what have you got to lose? Let them get as much sun as possible until the foliage dies down, and then slip the bulbs in your flower beds. They will take up no visible room, and if they come back, great. If they don't, you've supplied organic matter to your beds, which is better than just throwing them in the garbage.

It would be nice if you reported back next year how successful the experiment was.

The hyacinths can be planted outside. I've done it before and they have returned just fine. I planted deeper than the way they were in the pot.
Paperwhites are not frost hardy. I don't know how to go about trying to get them to rebloom next year. I've just tossed them after they are done.

The paperwhites won't make it outside. I've always accepted that it wasn't worth having a pot ghetto in the house in order to save them but you can try if you want. I like Bulbtone from Espoma - feed them per directions, place them in a sunny exposure and take care of them till the foliage dies completely. Do an online search about how to provide the right cold period of dormancy for paperwhites. It could be that you only need to store them in a cool place like you do for dahlias. If you feed them and take care of them, there are other white or yellow daffodils that would be more hardy for you staying in a pot, but I think all forced bulbs run out of steam at some point.

I usually take my forced daffodils and plant them outside after the foliage dies back or whenever I get around to it, fertilize with Bulbtone and find out later whether they made it or not. The forcing process takes the plant out of its natural cycle so they don't always make it.

With any bulb at all that you want to rebloom, it's important that they be well-nourished after blooming. Don't be in a hurry to let them go dormant, you want that foliage to be lush and green and healthy as long as possible.