It’s not very likely, but it is possible. These pesky parasites are not equipped to move through thick fur. Besides, human blood is their food of choice. As a rule of thumb, dogs (or cats, for that matter) do not carry bed bugs on them. If you’re dealing with a bed bug infestation, it’s possible you brought them in luggage from your travels. Another common way of bed bugs spreading is through used furniture, as they love hanging out on upholstered surfaces.