Public transportation is depressingly bad in the Boston area and not really an option for your trip.
Rideshare certainly works in Boston at that time of night. "Normal" price is about $100 but you may see significant surge pricing at night. Also, finding a ride from Providence to Boston on the fly might be risky. You can try to prebook on Uber and Lyft and see if they accept and what it costs. SafestThe safest option is a private car on sites like booking.com (no affiliation, but used successfully). It'll run you about US$200US $200.
Personally I avoid regular taxis, because I find them unpredictable and have been cheated way totoo many times. This would be more of an option of last resort.
Another alternative would be to just stay the night and take an early train. For example there is a Homewood Suites by Hilton that's a 5 minute walk from the station and cost $150-ish tonight.