If you 100% wish to not pay BAC, you should mention it in the listing right off the bat. This may result in decreased interest in the home, as some agents will not show clients your home because they aren't being compensated. If a buyer comes along that still wishes to use an agent, the buyer will have to pay their agent at closing. There's verbiage in buyer's agency contracts to cover these situations.
the first offer I received had a 2.5% commission owed from me to the buyer's agent.
In this situation if you believe it's a decent offer, you could counteroffer with raising the purchase price by 2.5% or 3% to account for the BAC + any additional taxes & fees associated with the higher purchase price. Or you could flat out refuse the offer with BAC and see if the buyers still wish to move forward while having to pay their agent themselves.
As someone who recently went under contract for a house as an unrepresented buyer, I can understand why buyer's agency can be useful for some, but in the end without BAC we made a stronger offer and preferred to work the deal ourselves. This made our offer around $8000 better by default.