There is not really a time limit, you just need to wait until the strip/tab has dissolved. Also if you need to take more then 1 strip, you should let them dissolve separately.
When they make people here do observed Sub dosing, they make them wait 5 mins, but I would think that as long as the strip has dissolved you'll be fine.
As far as the eating and drinking goes, most places recommend waiting about 30 mins to make sure that you get the optimal effects of the Suboxone.
If you want to get rid of the taste, maybe sucking a boiled sweet or mint would be better than drinking right after taking it? IDK?!