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Your bulbs won't be likely to get enough chill hours in the ground in San Antonio. Unless you are able to contact the company to find out whether the bulbs were pre-chilled, the best option is to dig them up and chill them in your refrigerator for six weeks, then plant them again. You should plant them by late December or early January, so you can use a shorter chilling period than the 12 weeks listed in the below article.

https://www.gardeningknowhow.com/ornamental/bulbs/bgen/chilling-flowering-bulbs.htm

If you have all ready began chilling the bulbs in the frig, you will need to continue to chill them for 16 to 18 weeks total.
Then you can bring them out and pot up to enjoy in this manner.
If you were to take the bulbs out of the refrig now, they would likely become soft and rot.
I have tulip bulbs in my own crisper drawer and will force them in water in a few months.

Here are some links to help you.

https://www.gardeningknowhow.com/ornamental/bulbs/tulips/forcing-tulip-bulbs.htm
https://www.gardeningknowhow.com/ornamental/bulbs/bgen/chilling-flowering-bulbs.htm
https://www.gardeningknowhow.com/ornamental/bulbs/bgen/flower-bulbs-in-water.htm

The tulip bulbs underground do not need light, so you can use the runner over them. Just be sure to remove it in the spring in time for the tulips to emerge (whenever they typically emerge in your region).

I highly recommend that you plant them as soon as possible and if you're lucky enough to get a winter day when ground temperatures are above freezing. Plant them in pots if that is not feasible. Spring will be too late if you live in the Northern Hemisphere. Tulips need to time (about eight weeks or more after planting) to establish a good root system before they send up leaves and flowers. Carrying tulip bulbs over until next fall is not a good idea.

Try to plant them within 12 months of when they were taken out of the ground. You may want to plant them in pots indoors or plant them outdoors next fall.
https://www.gardeningknowhow.com/ornamental/bulbs/bgen/flower-bulb-shelf-life.htm

Tulips can be difficult to re-bloom when they have been forced. It still is worth a try though!
I would remove the bulbs from the water and allow to dry in a cool and dry location.

You can then plant out into the garden this spring.

Here are some links to help you.

https://www.gardeningknowhow.com/ornamental/bulbs/bgen/how-to-plant-a-flower-bulb-in-your-garden-after-winter-forcing.htm
https://www.gardeningknowhow.com/ornamental/bulbs/tulips/tulips-care-and-tulip-planting-tips.htm