How can I see my bike in the game?
One way to do it is the mine/missile-view. Hit F5 in game to activate it, then lay a mine, preferably a pine mine for then the mine view is static. When you pass that mine you should see your bike in the view. However this is quite unsatisfying since you do not see the bike on full screen. To view your bike as others see it in the game, just start a multiplayer game with the setting
Record Demo: ON. When you replay the demo you can select, which bikers view you want to use when you playback the game. You can then see your bike from any other player's point of view. This might still not be as you would like to have it, for the other players keep moving or at least do not always have your bike in their field of view - at least if it was a regular deathmatch.
In this situation simply select to view player 16 from the watch player option by hitting the right arrow key and you will be able to fly around the level and see the game from a free-cam view.
[Note: If you switch view during the game you will not be able to switch back to player 16 view. It can only be selected before demo playback has started.]
related: [record demo] [flying freely around in a recorded demo]