With 28mm or 30mm lenses you will need to be relatively close to "fill the frame" with a bike and rider. TR4 Autocross 2009 Triumphest, San Luis Obispo, Calif.
50mm is a "short telephoto" on a crop camera such as yours. It is not equivalent to the human eye angle of view on your camera. (It is on film/full frame cameras.) On your camera, 30mm would be more equivalent to your eye's AOV.
Even 50mm will be a pretty short focal length to use for cycling.
You don't need terribly high shutter speeds. Unless shooting in low light/indoors, you really don't need f1.4 lenses.
In fact, it can sometimes be better to use slower speeds to leave some motion blur in the image... ranging from some motion blur from faster moving part of the subject, such as the wheels... to really motion-blurring down an unattractive background. For example, this was done with 1/50 shutter speed...
EF 70-200/2.8 IS lens at f16 and 200mm focal length. EOS 50D camera at ISO 100, 1/50 shutter speed. Handheld, available light.
As opposed to more fully freezing all movement with 1/800...TR4 Autocross 2009 Triumphest, San Luis Obispo, Calif.
EF 300mm f4 IS lens at f5.6. EOS 50D camera at ISO 200, 1/800 shutter speed. Handheld, available light.
When I'm photographing action such as this, a lot of the time I use two cameras: one set up with a faster shutter to freeze the action, the other set up with a slow speed to allow for some motion blur. It's harder and takes some practice to get good usable shots with motion blur, I always end up trashing more of the shots. Simply freezing all movement is pretty easy.
Since you only have a single zoom now (I'm assuming it's the 18-55 IS kit lens), I'd really recommend a zoom instead of a prime, so that you have more flexibility. My single most used lens for sports/action is 70-200/2.8 IS... but that's a pretty big, heavy, expensive lens.
If you want an inexpensive, fast focusing zoom lens that's not too big, has a nice range of focal lengths for the purpose... I'd suggest check here on POTN in the classified listings or on your local Craigslist for a Canon 28-135 IS. So many of these have been sold in kit with various cameras, there are lots of them on the used market and they are relatively affordable... often under $250 (they sell for close to $500 new, by the time you get the separately sold lens hood). They are USM, with IS, plus close focusing.... not your typical "kit" lens by any means. Much better made. The aperture is f3.5 to f5.6, but that won't be a problem shooting in normal daylight. Bump up your ISO, if need be.
When I have a hike or a bike ride with a camera, I'll substitute a 28-135 IS for both
my 24-70/2.8 and
70-200/2.8 IS. Saves a lot of weight and space! In any sort of reasonably good light, the 28-135 is perfectly capable of stopping action...Shortcut over 1st obstacle ACTHA Ride for the Mustangs 2011 - Hossmoor Ranch, Brione, Calif.
EF 28-135mm IS lens at f7.1 and 30mm focal length. EOS 7D camera at ISO 400, 1/1250 shutter speed. Handheld, ambient light.