Not sure, but as they seed themselves into very odd places including crevices in walls, I don't imagine the roots system can be very deep or wide.

Errr, yes they can.
I removed one last year and it was a very big, heavy, woody root - several large offshoots but the main one was a very large piece, probably about 18" diameter and the same depth .... and very heavy !
It had been in the ground about 3 years.

Oh dear! Isn't it strange that they cling on to walls, then.

It varies according to the soil type, variety of Buddleja, and the growing conditions, but in my experience, they have pretty aggressive roots, good at finding water in unlikely places--such as walls!