I'm curious about the cost of the bus vs. the cost of the bus. The (undiscounted) cost of the airport express is around 100HKD, or about $13 USD. How much do you save by jumping into a crowded / cramped bus?
I would imagine the bus would give a unique "local flavor", but I would imagine it to be more intimidating to a first-time visitor. I go to HK 2-3 times per year, and have been doing it for 10+ years, yet I'm not sure precisely where to go to catch the bus or where to buy the tickets. I'm sure I could figure it out, and imagine it is somewhere on the lower level in the ground transportation area, but I'd be looking with the benefit of having been to the airport many times. I only took the bus once or twice during my first trips to Hong Kong 10+ years ago when I was accompanied by my Chinese friends who didn't want to pay the "outrageous" cost of the Airport Express. I do remember that my big American carcass just doesn't fit well in those seats. :-)
The Airport Express, on the other had, is easy to find with a staffed counter, and only three choices of stops (Tsing Yi, Kowloon, and Hong Kong). It makes just one stop (Tsing Yi) between the airport and Kowloon, and has the electronic progress LED's displayed on the ceiling arch are probably reassuring to someone who has never been. From the Kowloon station, it would be maybe 50HKD taxi to Jordon? (I'd suggest giving a specific destination in Mong Kok / Jordan because without one it just looks like a bustling city street.) Those areas can be fun, but without knowing where to go -- and being alone -- what would a first-time visitor do?
The Hong Kong side is an equally good choice. For the first time visitor the more "touristy" things are not a bad choice as you can still get a flavor for the city, but not be overwhelmed. Take the AE to Hong Kong station, then a taxi to LKF (Lan Kwai Fong). While it's not necessarily a "Pure Hong Kong" setting, it IS easy to walk around there alone for a few hours in the active atmosphere loaded with ex-pats, western visitors, and hong kong residents. It's a fun experience. Or go to Times Square. Wander around in the lights and bustle, people-watch, and get a street-food snack. It's an easy walk from Times Square to the Excelsior Hotel, where you can go to the rooftop bar for a slightly overpriced drink and a view of the city.
The city doesn't really sleep much, so you can stay out pretty late. I'd just take a taxi back to the airport. Might not be the most cost-effective way at probably 400HKD (or around $50 USD), but it's probably the easiest at late night / early morning. Uber works there too.
I'd also suggest you think about a communication plan... make sure you know your carrier's international plan. Verizon has a $10 per day travel pass that lets your phone work there same as it does here. Probably easier than trying to screw around getting a SIM card. And be aware that the GPS/Maps on your phone can be spotty at times because of the tall buildings in the city, and it doesn't always seem accurate... or a times seems to be a little slow to react. I'd choose a destination before you go and get a little familiar with the area on a map BEFORE you go. That way it might be less intimidating, and your phone will be an AID rather than your only way of navigating.