This is a very good question, because it is hard to tell the difference between a bed bug bite and a mosquito bite.
First, look at the appearance of the bites. Are they in a line or clustered in groups of three or more? This is an indication that you could be dealing with bed bugs. While mosquitoes can bite more than one time, these bites will pop up in random places on the body. For instance, one might be on your knee while the other is located near your ankle.
Also, think about when you first noticed the bites. Bed bug bites generally appear in the morning, when you wake up from sleeping. Mosquito bites can appear at any time of the day, but the welts will start to raise up right after the mosquito bites you.