This isn't about how clean your home is
A pre- or post-move check is just practical timing: moving day naturally involves a lot of handling, which is worth a look regardless of how tidy anything is.
Before you pack
If there's any reason to suspect activity in your current home, an inspection before packing begins is worth considering. It's much easier to address in place than after everything's been boxed up and moved.
Boxes & furniture
Used moving boxes, in particular ones that have sat in a basement, garage or storage unit, are worth a quick look before they're packed. Furniture changing hands between a previous owner and a new one is one of the more ordinary ways bed bugs travel, so a check of any secondhand pieces before they go into the truck is a reasonable habit.
After you arrive
Unpacking a bit at a time rather than all at once, and keeping an eye on the usual spots, mattress seams, bed frame joints, as you settle in gives you an early read if anything came along for the move. If anything looks off, an inspection can settle it before it's had time to establish.
Common questions
Should I get a check before or after moving?
Before, if you have any reason to suspect something. It's simpler to address before everything's packed and moved.
Are moving companies a risk?
Not inherently, the risk is more about secondhand furniture and boxes that have sat in storage than the movers themselves.
I just moved and found something. What now?
An inspection can confirm what you're dealing with early, before it's had time to spread.
Do you check apartments before move-in?
Yes, a pre-move-in check is a reasonable request, especially for a previously occupied unit.