I've been to Brugge in November and May. November was very slow, dark and extremely cold. The wind off the North Sea does blow right into the area. March will still be pretty cool. I was in Holland from April to June one year. When I arrived in mid-April, it was 32 degrees and the tulips hadn't started blooming. If you could go in April vs March, it would be a bit better both for weather and for spring flowers.
I only visited Brugge on weekends. I haven't been to Ghent or Ypres. I would think that it would be a good center for touring. It can be busy during the day but it does get quieter in the evening since it is a frequent day trip destination. The streets in the town center are cobblestone and narrow but I think they would be fine to get around in with a bike.
As far as a rental,
De Drie Koningen has been recommended on Yahoo Travelzine. It looks very nice. According to their rates, March is split between low season and midseason. It doesn't look like they have a bike for rent.
I've worked in Holland a couple of times. Bikes are much more available there. Sometimes people would ship their bike via UPS instead of taking it on the plane. But I think that is pretty expensive. Since you are there for several weeks, you may want to look at bicycle dealers for longer term rentals or maybe purchase a used bike and try to sell it back.
A well known tour company which does both bus and bike tours is
Quasimodo. I haven't taken their tour but I've know several people who have. They say they are good although one person did remark that they were very opinionated.
If you do happen to go later in March or April, I highly recommend going to Keukenhof Gardens outside of Leiden. There are great rides around Leiden. In fact, I would recommend Leiden as a touring center if you go to Holland. It is easy to get out of town on bike trails or fietspads in Dutch. There are several day bike rides from Leiden such as to the ride to Katwijk where you can ride in the dunes to Scheveningnen near the Hague. You can ride to Keukenhof.
Here's an interesting
web site. It is in Dutch but you might find some information. I found a link for
this page which is in English and all about touring Belgium by bike along the waterways. It has a lot of information on cycling in Belgium.
I don't know much about Belgium beyond Brugge and Brussells but I know lots about Holland. Feel free to ask anything.