In a survival situation personal hygiene might not be as complete as it is during day-to-day life, but it should certainly not be ignored. Uncleanliness can lead to disease, infection, and parasites. Poor maintenance of one's teeth can cause excruciating pain due to cavities or decay. When building a bug out bag you should make some concessions for hygiene.
A toothbrush, and toothpaste if you like, will help to avoid cavities, tooth decay, and gum disease than can otherwise cause pain and tooth loss.
Bathing, whether it is a simple sponge bath or a full shower, is made far more effective through the use of soap and an ample supply of water. Many people such as Paul Wheaton follow a poo-less shower regimen. Meaning they don't use soap or shampoo during daily baths as they claim the nasties and dirties are water soluble and so they are washed away simply by scrubbing under a flow of water. They still wash their hands before preparing or eating foods and after using the bathroom.  
Cooking & Eating
Although modern society has a collective phobia about food safety and does crazy things as sterilizing cutlery and flatware after each meal it is till important to follow basic sanitation rules when preparing foods and cleaning up afterwards. Proper cooking itself is one of the main safeguard against food borne illness. Simply washing with soap and water of flatware and vessels used for drinking will help to keep disease in check.
Periodic washing of clothes will help to keep bugs from living in your clothes.
Relevant TSP Episodes
- TSP Episode 1180 - Saunas for Health, Sanitation and Grid Down Resiliancy
- TSP Episode 314 - Planning to bug in