Hey Ruth! If there are absolutely no signs of bed bugs (upon close inspection), its unlikely that they are the cause for the bite marks. I recommend taking another look for dark brown marks (dried blood) and other signs of their presence. Regardless, if you want to kill any bug on that mattress, just get a handheld steamer and blast it. The heat will kill everything and its completely natural. Hope that helps!
Unlike those of other insects, bed bug bites may sometimes appear in tight lines of multiple, small, red marks where multiple bed bugs have fed along an exposed area. Bed bug bites can cause itchiness. Initially, a victim may detect a slight burning sensation. The burning area then develops red bumps, known as papules or wheals (rash). In extreme cases, bites may swell dramatically or turn into blister-like skin inflammations.