Does an officer have the right to search a pocketbook during booking while the suspect is cuffed to a bench?

The police can search the pocketbook based on the following grounds:  Although the suspect was handcuffed to a bench, this search of the pocketbook could be a search incident to an arrest. It could also be construed as an inventory search so that the suspect won't be able to subsequently claim that items are missing from the pocketbook.  The search of the pocketbook could also be based on exigent circumstances requiring an immediate search because there may be a weapon or other items in the pocketbook which could endanger the police or others.  A search incident to an arrest, an inventory search, a search based on exigent circumstances are all permissible without a search warrant.