If I were going to try to save them, I would allow them to stay in the pot, with fertilizer of some sort until the foliage turns brown and the bulb is fed for next year.

I would pull them out and allow them to dry. Then I would store in a paper bag in a cool dry place, maybe a closet until October. Then I would chill in the fridge until Christmas and then plant, expecting flower about this time or later next year depending upon the type of tulip you have.

Caveat: When you lift the bulb, you may notice that instead of one big fat bulb, your bulb is more like a head of garlic...lots of little cloves. That is because the growers have allowed your big bulbs to grow but not flower for at least 2 years before they arrived in your pot. You may be disappointed in the flowers next year. Not simply because you went to so much trouble to deny that you live in a warm climate, but because it takes a long time to raise those gorgeous flowers.

Lest you think I am a opposed to tulips, I am in fact a bulbaholic and have planted 2100 tulips, again, this year.

Wishing you happy flowers
c

Wow that's a lot of tulips! thanks! Excellent information & I think I'll do just that.