One common theme could be adventure. Barry Bee might be on some exciting quests in the fanfic world. Another could be friendship, showing his bonds with other characters.
Yes, there might be some 'Shrek x Barry Bee' fanfiction out there. You can try searching on fanfiction websites. However, it's not a very common pairing, so it might take some time to find.
One possible plot could be that Barry Bee somehow gets lost in Shrek's swamp. Shrek, being the gruff but kind-hearted ogre he is, decides to help Barry Bee find his way back home. Along the way, they learn about each other's worlds and develop an unlikely friendship that could be misconstrued as something more by other characters.
I haven't read a particular 'barry bee fanfic' myself. However, if you search for it on platforms that host fanfiction, you can filter by the most reviewed or rated ones. Maybe you'll find some really creative takes on the character Barry Bee in those stories.
"What's the Secret of Lovesickness?" was a romantic, youthful-campus novel written by Si Yiqi Lu. It told the story of the female protagonist who hated the male protagonist's devilish face at first, but later fell in love with him because of her understanding and contact with him. I hope you like this fairy's recommendation. Muah ~š