Ride the bike.
First, you're looking at a 15-minute bike ride once you're used to it - if that. It's really not all that hard to be able to hold 20 mph or so on level ground if you've been riding steadily - and you're riding a bike built for that (which is really pretty much anything that's not a fat-tire bike or a MTB with knobby tires...)
Once you get riding more, you may very well decide you're going to "go the long way" as a mere 3.6 miles is pretty much just long enough to warm up.
Of course, that means you may have to shower when you get to work. So figure out how you'll do that if you have to. Because one nice thing about being able to shower when you get to work is that you don't have to worry about getting sweaty, or rained on, or muddy, or whatever.
If you're worried about how to ensure a reliable commute on your bike, read on.
Learn how to maintain your own bike. There's nothing hard about bike maintenance. Even building your own wheels from parts is easy if you just have a bit of patience. You just need some basic tools. Know how to change a tire - even if you never get a flat, tires do wear out. That means you need to learn how to remove and replace the wheels because you're not going to change the tires with the wheels still attached to the bike. Learn how to clean, lube and change your chain - chains wear out, too - and they wear out a lot faster if you don't clean and lube them (the exact lube used really doesn't matter - as long as you use a real lube, you're not strong enough to put enough heat and stress to cause a lube designed for automotive or industrial use to break down...).
Learn how to recable your brakes and shifters - cables wear out over time and you don't want your brake cables snapping right when they're stressed the most - when you grab the brakes and squeeze hard because you need to stop fast. Nor do you want your shifter cable to break and leave your chain stuck on the smallest rear cog with you having to get up a 10% grade with 20 lbs in your panniers...
Brake shoes or pads wear out too, and they're also easy to replace.
IMO that's all really basic maintenance that you shouldn't have to take your bike to a bike shop for. You can find video tutorials for all of it on the web - Park Tool's site has some really good ones.
Get a good floor pump with a pressure gauge on it, and learn the proper pressure for the tires - "as hard as you can make them" is not the proper pressure. For larger tires that can even be dangerous as a large tire at a high pressure puts a lot of stress on the tire bead that holds the tire to the rim - and in extreme cases the rim itself can fail catastrophically. The air inside the tires pretty much acts as a spring to make your ride smooth - a larger tire needs less pressure to work as a good spring. A good rule-of-thumb for max pressure is the pressure in your tires is too high if you feel vibration and hear road buzz on normal pavement.
In order to commute reliably by bike, you need to be able to address mechanical issues that may crop up. Flat tires, obviously. More than one. So you'll need spare tubes and a way to reinflate your tires. You're commuting, so time may be important. CO2 inflators work great for that - just be sure to put enough into larger tires. You'll also need a pump on your bike (for when you screw up the CO2 inflation process and squirt all the CO2 into the atmosphere because your hand is wet from sweat and the CO2 cartridge slipped...) Two spare tubes and a patch kit are probably overkill for flats, but the ability to address at least two flats is pretty important - what are you going to do if you get a flat on the way to work? Another important thing - tire boots in case you run over some nasty debris that gashes your tires so badly they can't hold the tube in place.
In case your chain snaps you'll need a multi-tool with a chain breaker, a few "missing link" chain links, and maybe a 3-4" bit of chain. Make sure your multi-tool has a spoke wrench on it in case you have to deal with a bent-out-of-true wheel or a broken spoke.
So you'll need a good-sized tool bag on a commuter bike. Toss a handful of nylon tie-wraps in. You never know when you might need some to keep in place a busted water bottle cage caused by you allowing your bike to fall into a guardrail.
For a commuter bike, ride wheels with a lot of spokes. If a spoke breaks on a 32- or 36-spoke wheel, you'll probably be perfectly fine to either remove the spoke entirely or just wrap it around other spokes to keep it out of the way. If a spoke breaks on a 16-spoke wheel, you may very well not be able to use a spoke wrench to get it true enough to ride on at all.
For a flatter commute, a single-speed bike makes a lot of sense. Chains on single-speed bikes are thicker and stronger than chains on bikes with multiple speeds.