Spring bear hunting is great fun, but I usually do it earlier than June.
It's generally done by stands over bait. A lot of outfitters are geared up to hunt only from mid-late afternoon and evenings. After the adventures of the day are told hunters might not turn in until midnight. Mornings are often spent refreshing baits, practicing with your bow, and skinning any bears taken the night before.
I would expect the blackflies and mosquitos to be quite bad. You would want repellant and maybe a headnet, light gloves. It could be warm, so I would suggest lightweight clothing that covers exposed skin.
This is just my experience. Your situation might be different. Your outfitter probably told you all this anyway.
I will tell you one thing. Even if you are an experienced hunter, after you sit in the stand watching for a few hours, or even a few days - when that black critter appears your heart is going to pound like crazy and you might feel like you can't breathe. Be prepared to get a bad case of the shakes.
Is it a fully guided or independent hunt?