Having a submissive dog definitely has its advantages, especially when it comes to grooming time. In most cases, a submissive dog will simply stand there and let you groom them, bathe them, and do pretty much anything as long as you are not hurting him.
While your passive pooch may not mind you doing most things to him, when it comes to bathing and grooming, he might still be a little skittish. Take your time, let him set the pace, and use lots of treats to make sure each grooming session goes smoothly.
Many dogs don't really like being groomed, submissive or not. Your pup probably thinks his tongue and teeth are all he needs to groom himself and look just fine. All it will really take is being willing to work with him until he finally gets used to being groomed on a regular basis. While you need to groom him once a week, be sure to check with your vet to see how often you should bathe him. Some breeds should not be bathed more than once or twice a month.
Grooming a submissive dog should be a relatively simple process, they should hang out while you do the grooming and not fuss much. But you can always use treats and kind words to keep your pup in the mood and pay close attention when you are working around his sensitive areas to keep him from getting nervous. Make grooming fun and use it as a bonding time for both of you.