It sounds like you've taken in a dog who wasn't treated well in the past. The biting, bowel movement holding and aggressive behavior, especially in a Beagle, sounds typical of a dog who's nervous and fearful. Lots of reassurance, kindness, reinforcement of good behavior and gentle, but firm, correction of unacceptable behavior will most likely take care of these problems with time and patience. Do keep him supplied with plenty of squeaky and chew toys to satisfy the chewing urge, though. Puzzle balls are great helps, too. They really keep them busy and interested, trying to figure out how to get those treats out. A Kong toy filled with peanut butter is also great.
The only thing that would really worry me about the shy bowel movement problem is that he might become constipated. Praise him lavishly when he goes. My guess is that someone has abused him for going in the yard or has been extremely harsh during house training.
Dogs are scavengers by nature, so the love of garbage may or may not be the result of not being fed enough or mistreatment by his previous owner. A spray bottle to squirt him with, along with a firm "No!" whenever you catch him in garbage might help. Another dog owner here is using a squirt bottle to correct a dominance behavior problem and is getting good results. As he gets more secure in his new home with you, it will become easier to correct his behavior. When you take him out, try to get him involved in a game of some sort to get him used to the idea that there is more to the outdoors than garbage.
As for sleeping on your bed, well, it sounds like he's becoming attached to you and his new home very firmly. Has he got a bed of his own? You might try putting an old T-shirt or two that has your smell on it in his bed. You may just have a little dog that sleeps on your bed, though!
Every bit of love and effort you put into your little Beagle will be returned a thousand times over. Keep at it and enjoy your new life with your new best friend.
Maybe Mason's will see this thread and give you some better advice. How 'bout it Mason's?