Oh jeez, a uniform... I don't know how I'd deal with that one. Everybody knows how you look normally, and then all the sudden, you sprout a belly overnight. I understand how people might start asking questions or why you might be very worried about them figuring out you're pregnant way before you're ready to tell them... I've been thinking a lot about this question and thought I could give you a better answer than "hide the bloat belly!"
Some of the bloat could be caused by gas, since we are sooooo gassy during pregnancy. I know some of my bloat was in the beginning. Some extra walking and avoiding foods that are hard to digest and carbonation could help with that. Fatty foods and soda cause me to bloat so much more when I'm pregnant. Also, constipation will definitely cause bloat. Probiotics, maybe stool softeners if needed to stay regular (and probiotics boost your immune system and help keep Group B Strep away!). Doctors always say "eat a fiber-rich diet during pregnancy to avoid constipation," but that crap has never worked for me. haha. A really good tip, though, is to try drinking hot water with lemon about half an hour before meals... at least when you're at home.
Most of my bloating tends to be water. Drinking more water than usual might help and is absolutely necessary during pregnancy for me. I drink a lot more water when pregnant, or my Braxton Hicks get stronger (being it's my fifth baby, they're strong enough on a good day!). I make sure to stay very well hydrated.
You're right there with me having back-to-back babies, so if the extra large belly could be caused by a well-loved uterus or stretched bellies/ligaments, we're probably screwed. Sooo.... I'm not gonna promise that any of it is actually going to help the bloat, but they're all good for pregnancy and digestion and overall health, so it can't hurt to try.
