Legally, how would you describe 'riding' a bike?

[David]

A bit of story behind the question and I could not find any clear info anywhere. I was walking / carrying my bike down through to the subway / metro when I reached the area to pay (there were four sides to pay from but only 2 access points for wheelchairs & bikes) I waited in line at one of the access points a few ladies jammed up the system, I ended up waiting a good 10 minutes before I decided that it was probably best to just go around, so what I did was not ride my bike but I sort of scooter walked it around to the other side. I put my foots on one pedal and pushed off the ground. When I got past the point of pay the first thing I see is two groups of about dozen Police officers each. As I pass them to bring my bike down to where the tracks are, two officers call me over, they ask for ID, after asking why? They say that I am not allowed to ride my bike in the metro/subway. They find me 75$ plus admin fee to total of 100$. Is this case worth going to court over? When I looked over the Law R-036 here in Montreal it says riding a bike or a scooter in the metro/subway you can be fined. With over dozen officers there would there be any way to fight this fine? or would it just be best to pay the fine and move on. The only thing is I don't find that what I was doing was riding a bike. I was just annoyed at the jammed system and wanted to catch the next metro train and was forced to go around. If the STM had a better system I would not of been forced to go around and would not of even scootered the bike? Should I write too the bus/metro company about this? would it be possible to recieve compensation for the fine from the company even if I pay the fine to the police? A lot of questions but please don't reply if you don't have usuful answer.