It's way easier than you think it might be. I biked from Denver to New York City a couple years ago and it's really amazing how easy it was.
-That said, invest in a high-quality cycling bib with chamois. Like, go to a specialty store and spend $100 on it. You will thank me. I used one pair during my entire 2-month trip and not ONCE did I ever experience a sore on my perineum.
-You don't need fancy-ass cycling shoes and lock-in pedals. A pair of comfortable shoes will suffice, but DO get straps for your pedals. Makes a huge difference in how much energy you use while cycling.
-Bring a small cleaning kit and give your gears/chain a light cleaning at least twice a week. You're putting a lot of miles on a bike compared to any riding you do for fun in the city.
-Get a high-quality pair of tires for the bike if it doesn't already have one. For comparison, the stock tires on my bike lasted 900 miles before practically disintegrating whereas a new pair from Giant were hardly worn when I finished 1100 miles later. Needing a new innertube on the road is no big deal. Needing a new tire can be a trip-ender. One of the stock tires broke while I was in small-town Missouri, and the closest shop that carried 700c tires was 94 miles away, and I had to spend an entire day looking for a ride. If I hadn't met a nice church pastor, I might have had to do dark shit to get a ride.
-Get a small bike computer, even a cheap one from Walmart. The odometer is extremely useful for navigation, and the speedometer really helps you find your most efficient gearing, as well as also aiding in navigation.
-Other than that it's not much different from a hiking trip, and the gear you bring is almost identical.