I don't think a bodybuilding routine would go too well with boxing.
Yes, you would be able to put on size and muscle, but it wouldn't really help your boxing unless you want to look muscular and aesthetic. The problem with this though would be if you were to compete as with bigger and bulkier muscles you might push yourself to a higher weight category if you plan to fight. When you're in a higher weight category you'll likely face opponents who are taller and have more reach, which won't be fun.
That being said, you can build muscle even if that would push you to a higher weight category, but then I'd recommend looking for a strength training program that is aimed towards martial artists and combat sport competitors. Heck, even types of strongman could give you amazing results. This way your muscles won't be there just for looks and believe me you can look as aesthetic as with a bodybuilder routine.
It's important to weigh in your goals though and realistically look at how you should proceed. You do box a lot in a week, so maybe you could ask some of your peers/trainers at the boxing gym how they would go about it when it comes to adding weightlifting to a boxing regimen.
When looking at a program though you should keep an eye on compound movements vs muscle isolation. Compound movements will build your athleticism more than exercises that single out a few muscles.
Hope that helps!