Your commute sounds similar to mine. Mostly a rail trail next to a lake through woods and some quiet lakeside neighborhoods. Plenty of animals to look at. 4 miles is nothing! Yes, why WOULDN'T you?
It shouldn't take you 45 minutes once you've been doing it for a little while. Maybe you need to get your bike set up to fit you better? Or tuned up? Something as simple as a seat height adjustment can make a big difference in efficiency.
Think about the money you'll be saving... Gasoline, for one. If you ride all the time, you can truthfully drop your insurance to "recreational use only" for some good discounts. If you pay to park, there's another savings. Not to mention the annoyances of rush hour driving.
Ride!
