You have a couple of choices. You can just bump it up to a larger container with just water and maybe some pebbles or marbles for stability or you can plant it up like a houseplant in a container with a drainage hole and decent potting soil.

Either way, you should gently loosen up the roots a bit before upsizing. That's a very healthy looking lucky bamboo and the root mass is atttesting to your good care.

Here is a link that might be useful: growing lucky bamboo

Hi, Gardengal48,
Thank you! As you advise, I think I will just bump it up to a larger container and just gently loosen the roots a bit. I guess I don't want to shock it and make it unhappy by doing anything as drastic as putting it in soil, as it has been happy up till now.