I am seeking advice on what to do now.
I have had this one since 2017 and it produced two 10" stolons with new pups. These pups sitting on the long stolons flowered this year and are now producing stolons of their own.

I understand this is a terrestrial type Bromeliad. Would you just plant in the ground and let it do its own thing naturally?

That's a type I've never seen! If you leave it to do it's thing, it'll probably end up a very messy clump. I probably would try to root the pups and keep it more orderly. With that one, I'm not sure it's possible!

Karen, I can not find much information online for this Billbergia.
Do you think I should try to root the already flowered plants or wait until the newest pups reach a size? The original plant is producing a new stolonifera pup at this time also.

Here is a quick look at the original tired plant pushing a new stolonifera pup still.

I have absolutely no experience with anything like this, but I think I'd go ahead and root the bloomed out pups so they could make a bunch more. I'm sure anything you choose to do will be fine. I certainly would love your climate! My broms will be coming out this week for their summer vacation.

I have that plant, mine is variegated, I didn't realize it was terrestrial. I hadn't looked at mine for awhile since it bloomed, pulled it out and checked it, I have four stolens (one is a good foot tall), they're growing straight up and not out to the side like many do, but that could be where I had it located, was in a deep shaded area, maybe reaching for the light?

Very interesting plant, I will have to leave mine in a pot, don't want to take a chance of losing to a freeze. I'm thinking it would make an interesting hanging basket. Here is a photo of mine I just took, you can see how tall the stolons are, I kind of like stolon plants hanging, so I think I'm moving mine to a hanging situation, and maybe the stolons will fall more to the side. Whatever you decide to do, keep it posted, not much info on this plant, but glad you brought it up, I might have not realized mine was being cramped where it was...but does seem to enjoy shade.

@Scotti I looked back at my original plant, this may help you out Scott. This was two years ago and they were just cuttings off the stolon, no roots, you can see their size by my hand. So you can just cut those and put them in the dirt...that's what I did and you can see from my last post how much it grew in two years. Cool.

Thank you Sherri! Yours looks great! I removed mine out of its sun location today. I will wait a little longer before rooting the new pups as they are small at this time.