Bed bugs are very difficult to see in carpet.
They are nocturnal so they generally come out after lights are out at night. They are elusive in that they do not like to come into open areas that might allow for their discovery. Bed bugs have flat bulky shells. When fed, the bed bugs can swell to appear more cigar shaped. They are also transient in that the bed bugs are experts at hitching rides to other areas of the home or worse, other buildings. This makes it very difficult to find bed bugs in carpet.
Bed bugs are small, only 3/16 of an inch when fully grown. They are also flat, which allows them to hide in places that many insects cannot squeeze into. It would seem that carpet is a natural hiding place for bed bugs. True, adults will easily fit into the nap of the carpet. Juveniles or nymphs will also fit into folds of carpet. Finally eggs would easily fit and be secure in carpet.
Although there are cases where bed bugs can be found in carpet, there are reasons why carpet might not be the preferred habitat for bed bugs. However, they can be found anywhere near humans.
Bed bugs like to stay near their hosts. They prefer beds in a typical household or living room chairs if the family spends time sleeping there. Bed bugs conserve energy and do not move great distances to the host. There is no reason for the bed bugs to infest carpets when they can infest areas near their food source, humans.
Perhaps bed bugs prefer humans because we don’t have thick fur such as other animals. The thick fur might allow the host to discover the bed bugs as the bed bugs move and brush aside the thick hairs of fur. Many animals use fur to sense movement and that would be detrimental to bed bugs. Bed bugs do not move easily through thick fur as the hairs also create significant obstacles. Nymphs might move through carpet easier than adults, but mobility is also difficult. Bed bugs eggs are glued to surfaces near hosts and carpets are not ideally suited for egg laying.
There also might be shampoo or even organic materials used in carpet production that remains in the carpet. This would create an inhospitable environment.
So while bed bugs could survive in carpet, their biology and habits do not make carpets the ideal harborage points. While it might be possible to find live or dead bed bugs on carpet, the carpet is rarely infested. If bed bugs are in carpet, it is more likely that they will be found at the perimeter of the room.
Evidence of bed bugs on the wall and carpet of a home: