Bed bug bite appearance
A bed bug bite is painless and some people have no reaction to the bites at all. Most people have itchiness, red spots, or welts (linked image from the Daily Mail, UK) that look like mosquito or flea bites hours later. There may be an itchy bump but the tiny bite mark may not be visible. These usually fade after several days. A few people have severe allergic reactions.
Bed bugs usually bite at night while you are asleep. If you wake up in the middle of the night and find a bug on your bed, don't squash it - instead, completely seal a live sample in a clean zip-style sandwich bag and have the bug identified by a pest control operator.
Bites are only a clue that you may have bed bugs, but you can't tell from bites alone that you have a bed bug problem.