It sounds like you'll be in Bellagio for at least a night or maybe more.
You can go back and visit after you leave the bags at your hotel in Bellagio.
It's a short relaxing 15 min ferry ride and ferries are frequent. It's not that expensive. The boat fare is 4.60 euro per person one way (3.70 euro if you are over 65 and travel Mon-Fri). There is no luggage store in Varenna, and if there was one, it would probably be more expensive than the round trip boat ride. Besides, it takes 30 min to visit Bellagio and even less to visit Varenna. Just enjoy the ferries. They are very relaxing. Try Menaggio too. They have classical music on Piazza Garibaldi every night (if you go in summer). The only issue might be going back across late at night (just take a taxi boat)