Is Buying a Bike a Necessity in the Netherlands?
The answer is no, but you'd be a lot better off with one as far as convenience goes. The Dutch bike literally everywhere. Before I even left the states for Maastricht, I emailed back and forth with a classmate of mine that was studying as an exchange student at Maastricht University the semester before me. When I asked her for advice, she couldn't stress enough how important owning a bike was. Her exact words were "It's almost weird if you don't [ride a bike]." And she wasn't wrong.
But that doesn't mean that you absolutely have to purchase one. I personally did not need to buy a bike, mostly because of how centrally located my apartment was to the train station and all of the major city sights. I did, however, consider getting one for social purposes since all of my classmates in Maastricht rode their bikes everywhere while I was that guy that was stuck saying "Okay, I'll just hop the train and meet you guys there!" whenever we wanted to go anywhere together.
If you decide to invest in a bike, you'd likely be able to get one for a pretty decent price (anywhere from $35-$70). There's a whole Facebook page dedicated to the buying and selling of bikes in Maastricht. Since there are so many students coming and going, there are always bikes being sold and handed off to new owners.
The downside of such a simple buying/selling process is that you run the risk of purchasing a bike that doesn't work well or could have been stolen. You can never be too careful with buying things unofficially so it's best to come prepared and have the owner of the bike you're ready to buy sign a release waiver with their contact information showing that you bought the bike in good faith without any prior knowledge of misconduct.
That way, if you get accused of having stolen the bike, you can show proof that you bought the item under the impression that it was a legitimate purchase. It'll save you a lot of trouble in the long run.
It’s totally your prerogative whether you decide to buy a bike or not. In most cases, biking provides an even faster mode of transportation than cars. If you find yourself living in close proximity to work/school, I would greatly advise the purchase of a bike rather than dipping money into an OV-chipkaart (travel card used for public transport in the Netherlands).
For certain cities, I really don’t think a bike will be necessary at all. For instance, I saw more cars in Amsterdam than I did bikes, leading me to the conclusion that it’s probably a lot easier (and safer) to avoid bike usage there entirely. But that’s coming from someone that is not at all used to riding alongside cars, so perhaps I am not the best authority on the matter.