First you must determine what the red bumps are a result of. With a physical exam, your physician can determine if the bug bites are secondary to a inflammatory reaction, allergic reaction, or if it is secondary to bug bites. Only after you determine the cause of the bites can you begin treatment.
Given that the lesions are distributed throughout the body, it seems likely to be a systemic reaction and less likely to be bed bugs. However, fleas may also produce a similar pattern.