How do I find the answer when it arrives?

I'm sorry to ask the question, are you sure they are Penstemons? When you say that they spread like weeds and have an enormous root system; it makes me wonder if it is something else. You don't mean Pennisetum which can become an invasive grass.

Hi Jenny and welcome to GOY. It might help if you could post a photo of them. Any replies as you have probably already seen will come up under your question but if you also click on the top bar that has "Hi Jennydaniel" with "your options" next to it in a white box, when logged in, it will take you to your home page. There is a bit that tells you, you have had replies. If you then click on that, it will take you to the replies. Hope that makes sense :-). Jen

Hi Jenny, Welcome to Goy! I'm wondering if they are Phygelius...the roots on them will travel right across a garden! I shouldn't think Penstemons would do that. A photo would be great :)

Have you tried Googling Penstemon Images? You can check there whether this is the plant you have. They get very leggy and fall over in the winter if not cut back but they do not spread or behave in the way you describe.
When we are sure what you have we can hopefully make some suggestions.

Hi, welcome to GoY from me too, I hope you haven't got what Karen suggests, but it sounds as if it could be, it gets fairly long, slim, trumpet shaped flowers, similar shape to penstemon, very hard to get rid of, because the roots get into every nook and cranny, and they just send up new shoots, common name devils tears, if they are, you'll find out why, Derek.

Lol Derek,mine just died!

Hi Sue, weren't you the lucky one, can't get rid of mine, but I've managed to contain them to one area that doesn't get any sun apart from just before sunset in summer, and none at all in winter, Derek.

There were some in my patio border when I came and nearly 4 years later I still get the occasional shoot.