Are there bike rentals near the train station in Vernon and is it possible to tour the gardens with a bike?
There is a coffee shop right across from the train station in Vernon where you can rent bicycles for the 4-mile trip to Giverny. It's a pleasant, easy ride. You cannot take bicycles into the gardens, but there are bicycle racks outside where you can park your bikes. My sister and I biked to Giverny when we visited France, and it was one of the highlights of our trip. Hope you get to do it too!