After staying in an apartment in Barcelona for a week, we plan to stay in Girona 2-3 nights before leaving from BCN on a mid-morning flight. What is the best way to get to BCN from Girona? Would it be better to go back to Barcelona for the night before we leave? If so, is there any hotel near the airport?

There is a direct bus service from Girona to Barcelona's El Prat (BCN) operated by Sagalés but the times aren't very convenient. *And the bus ride on the 602 takes two hours. There's a departure from Girona's bus station at 6:45 am, arriving at 8:45 am. What time does your mid-morning flight depart? * The next bus doesn't arrive El Prat until 11am.
https://www.sagalesairportline.com/en

A quicker way-- you could take an early morning AVANT train from Girona to Barcelona's Sants station (a 39 min. ride), then taxi to the airport (under 30 min.)
Renfe

But to err on the safe side, to feel more comfortable, I'd be inclined to spend the previous night in Barcelona.
If you don't want to spend your final night in the city, there's the BAH Barcelona airport hotel and the TRYP with free airport shuttles, but I've never stayed at either.

*

Thanks once again for such helpful advice. We will check trains and hotels and likely not do the bus.

marsha,
If you want to check the price of a private transfer from Girona to El Prat, this company specializes in this very thing. They're local, Taxis Carreras, and not a middleman.
Taxis & Shuttle Girona - Taxis Carreras

Private transfers are never inexpensive, but they'll get you there on time if you don't want to change hotels to spend your final night in Barcelona.
The Girona airport site estimates the cost to be 150 euros weekdays and 165 weekends/holidays.

Thanks. Great advice from all. We are equating costs/comfort etc. before making a final decision.