I have had experience with snoring dogs. When I exercise my dogs all day, especially right before bed, they tend to be so outrageously tired that they snore all night (but not too loudly that it keeps me up). My advice is to not exercise him extensively before bed, give him like an hour or so of rest. This way, when he sleeps, he isn't as tired when it is bed time. Then, hopefully, when he rests, he won't snore.
If your dog is on the heavier side, it could be due to excess tissue in their airway. One piece of advice given is to exercise them regularly, which will reduce weight and snoring. Check out this website: 6 ways to stop dog snoring.
Snoring could also be caused by a cold or allergens. If it is allergens, make sure the bedding he sleeps on is clean and dust free. It may also just be the breed. Some breeds are more susceptible to snoring (like pugs or Boston terriers). In which case, it may be difficult to stop them from snoring.
PART 2 (ADDED): Ok, so I researched more on Boston Terriers and their snoring habits. It is due to their breed and you can't do much about it. Check out this website: Reduce Snoring. My advice after looking through this and other websites, is to change the position of how the dog sleeps. If the dog is laying on their back, then their snoring will be more noticeable. A recommendation is to get a round dog bed so they sleep in a ball -- which reduces snoring as there is less pressure on their throat in the night. However, I know you want the dog to sleep in the room with you, so I would make the dog move positions if the snoring is bothering you and attempt to train him to sleep on his side or stomach, etc.