Most parasites are extremely host specific, though there are some exceptions. I dont think a bedbug would go for any reptile, though I could be wrong.
Give your BP a good soak and see if any endo-parasites drown. Also give your BP a good look over. LOOK CAREFULLY. Mites are small, but if you know what your looking for it can be relatively easy. Tics should be easy to spot. They are larger than mites, and are pretty unique. They are flat bodied since they are herp tics.