I've yet to investigate fixing my underbed tents, however I was considering some kind of drawstring afair, using a loop of cord to which the underbed tent can be attached.
The cord can then be pulled over the bed base such that its circumference is narrower than the edge of the bed base. A knotted loop and small d-clip would be used to secure it
Like I say, yet to try it as waiting for warmer weather to set the tent up (was busy this bank holiday), all fabric parts including the awning are still safe and dry in the loft.
What kind of bed base is it? Our underbed tent actually came supplied with the wrong fittings for our slatted bed, so I gave those away and made some loops. What we were given was some little 'U' shaped brackets which screw to the bed boards, and the underbed tent simply hooks onto them. Since we had a metal framed slatted bed I used some short lengths of guy line and toggles to create adjustable loops to hang the tent from. It's worked fine.