The sure way to get a blown out bg is to point a flash or light at it.
Not knowing your setup it's hard to decide what to do.
Yes...we don't really know "what" you have to work with. if the background is white muslin, it ought not take much flash power applied to make it WHITE in the final shots. If you have even 1 f/stop more light light (incident light reading) than the subject (also incident light), then a white cloth is gonna be white in the image.
You can also lift the highlights a bit in post, to make sure the white is pure white. You do not need to literally or figuratively "blow it out"...you do not need to "NUKE" a white fabric to make it white. In fact, if you just use LESS LIGHT ON THE SUBJECT, the background will automatically be what is called key-shifted, to a higher place on the curve...and the backdrop will automatically be pure white.
This is a very simple process,
key-shifting, that experienced studio shooters learn. It was a Dean Collins lesson 30 years ago in Peterson's Photographic. Instead of trying to apply more and more and more flash power to a background, the easier solution is to apply LESS light to the foreground subjects, and thus increase the differential.
The difference between foreground and background is what is important--not the absolute amount of light being applied!