If gently flushing with sterile water doesn't get it out, you could try getting some plain sterile saline eye drops in the morning and try those. But if you aren't successful, yes, I would suggest getting your bun seen by an experienced rabbit vet.
Something else to consider, is if the hay is very abrasive, the longer it's stuck in the eye the greater chance it could scratch the cornea, which could result in a corneal ulcer. So if you don't end up needing to go to the vet to remove the piece of hay, still check the eye regularly for any signs of continued irritation and/or any white clouding starting on the cornea, and get your bun seen by the vet if there are any problems or concerns.
Medirabbit: corneal abrasion and ulcer
https://rabbit.org/veterinarians/