I can recommend best time to visit NE Poland depending on your expectations and tailor-make an offering for you. An all-inclusive trip with full-boarding accommodation, transport, entry fees to National Parks and guidance is also available, as well as an extension to Belarusian part of the forest for Great Grey Owl.
If you don’t search for a guide but only for an accommodation, then take a look at my friend’s four-person apartment that is a perfect starting point for exploring the Białowieża Primeval Forest by yourself.
Usual price for guiding service is ca. €200/day (the price mostly depends on date of visit).