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!
Bed bugs were mentioned in ancient Greece as early as 400 BC, and were later mentioned by Aristotle. Pliny's Natural History, first published circa AD 77 in Rome, claimed bed bugs had medicinal value in treating ailments such as snake bites and ear infections. (Belief in the medicinal use of bed bugs persisted until at least the 18th century, when Guettard recommended their use in the treatment of hysteria.[51])
Wash all the clothing that you brought home in a washing machine. Even clothes that you didn't wear must be washed in hot water. If you cannot wash something in a washing machine, you can either place it in a hot dryer or seal the items in a plastic garbage bag. If you seal items in a  garbage bag, leave the bag securely closed in an extremely cold or hot place for a few months.
Both of these types of Hemiptera are sensitive to extreme temperatures. It may be necessary to rid the infestation by exposing the area to extreme heat or cold; they are most comfortable in temperatures around eighty degrees Fahrenheit. Raising the temperature to ninety-seven to ninety-nine degrees may kill off a significant portion of the population.
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.
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