Mokummer, with all due respect...
she heated and cooked on electricity
But the same applies to many households here in the Netherlands, doesn't it? I need electricity too to get my CV-ketel started, otherwise I won't have any hot water and consequently my central heating doesn't work.
since she had to work as a cleaner at 6 different addresses, also out of town, she did need a car
Contrary to buses and trains, my car departs when I want to depart, so if I had to visit 6 different out-of-town addresses on one day, I wouldn't travel by public transport either; and that's me living right in the middle of the Randstad - believe me, there are several areas in the Netherlands where 1 bus per hour is considered something of a luxury.
we both did a trip to the same address recently in france - and by thalys, from schiphol, i can be there in little over 3 hours. she had to go to brussels first which would take her more than 2 hours
By the sound of it you are comparing apples and oranges - from your handle I take it you live very close to Schiphol; had you been living in, say, Zwolle or Alkmaar or Den Bosch, you'd have to travel over an hour too before you got to Amsterdam CS or Schiphol to take the Thalys.
To the OP: Maastricht is connected to the railway network and has several trains per hour to anywhere in the Netherlands - see [www.ns.nl] for timetables and fares. Every city worth its salt has an excellent network of public transport, and Maastricht isn't that big; if I were you I wouldn't bother with buses and just get a bicycle to get around as you are already planning to do.
Also, make sure you get an OV Chipkaart ([http://www.ov-chipkaart.nl/?taal=en]) for public transport.