I do the Boston to NYC trip frequently for matinees. I don't use the bus, most frequently travel by train. I live in the Boston suburbs so I use the Rte 128/Westwood station. For me is so much easier than going downtown to South Station. It is a breeze to get in and out of and parking is always plentiful. On weekends, you can park really close to (literally within steps of) the station's entrance I've driven into that parking lot literally 5 minutes before the train was due (overslept!) and still made the train (don't recommend that though). About $15 for parking
My usual routine is to take the 6:46AM Regional Amtrak which normally gets in (in my experience) at about 11:15AM, though published arrival is 10:53AM. Yes, yes it's early, but I grab a Starbucks and breakfast sandwich and settle in the Quiet Car (a must when I am by myself). With great reading/listening material it is actually quite relaxing because it is soooo quiet--you can snooze too. I have never missed a matinee with this train. Wi-Fi is sometimes spotty. I then have time to get something to eat before the show, take a stroll or do a quick in and out at MOMA. On Saturdays, I've never risked taking the next Regional (at 8:40AM) which gets says it gets in at 1:03PM but which more likely means 1:30PM (on a good day) and that is cutting it too close for me. (I've never had an Amtrak arrive on time in NY despite almost always on time departure, though have never been more than a half hour late arriving). For Sunday 3:00PM matinee the 8:40AM works. On a nice day I walk from Penn station to the theater or otherwise take the subway. I take the 5PM or 7PM train home depending, of course, when show ends.
Though I've splurged on Acela once in awhile, it is not worth the extra money to me, when, generally, according to published departure/arrival times, the trip is only about 35 to 40 minutes shorter. Certainly you can leave later in the morning if you are Acela inclined.
I only use the Saver fares which (for Regional) which I've gotten as low as $39 or $49 when there is a sale (and there are frequent sales). If not on sale, the Saver price does now hover around $56, as others have noted, but usually you need to book about 3 weeks in advance for the lowest Saver. Those fares go quickly and are not usually available or they are not as cheap if you book last minute. Sign up for the Amtrak email and you will be notified of sales. Also sign up for Amtrak's guest rewards program if you plan to use the train regularly. I have been able to earn several free BOS/NYC trips with rewards points.
On occasion, when I couldn't make the early Amtrak or when Penn Central Station was experiencing horrendous outgoing delays a year or so (or more?!) ago (and if you have a car or friend with a car) I have driven to New Haven (about 2 1/2 hours) and taken the Metro North to Grand Central (about 2 hours -weekends usually about $35.00 round trip, I think parking is about $14) then subway to theater (or walk if its a nice day and show is not at the Public). The parking lot at New Haven also has a relatively easy in and out and is attached to the station entry. Takes a little more time but it is an option when circumstances dictate.
Also, if you have a car, I have on occasion driven in (usually or a Sunday matinee when the weather is nice and the show is at Public or in the Village and could not get a Saver Fare) and always find plenty of great free! street parking, grab a meal at a bar after the show and then drive back. That is a lot of driving, but I like to drive (god bless Audible if I am by myself) or share driving duties with friends or family. Every once in awhile, driving back and forth on the same day does not bother me but it is not, I know, everyone's cup of tea.
The one day back and forth, even by train, is not for everyone by I find it a very rewarding ritual especially when the show seen is worth the time and effort. Enjoy!