21202 is discussing the position within the lane(s) that a cyclist can ride. You cannot take 21202 on its own without considering the rest of the vehicle code. 21650.1 states that a bicycle shall be operated in the same direction as vehicles are required to be driven on the roadway. So, California Vehicle Code says you cannot ride against traffic on a one-way street if you are on the street, shoulder, or bike lane (if present).
However, the City of Los Angeles has local ordinances that govern bicycle riding which allows you to ride on the sidewalk, but does not specify a direction. I suspect, but am not certain, that you can ride against traffic while on a sidewalk within the city limits of Los Angeles.
Clear as mud? A good place to start on California Vehicle Codes governing bicycles is the CABO website.
(a) Any person operating a bicycle upon a roadway at a speed less than the normal
speed of traffic moving in the same direction at that time shall ride as close as
practicable to the right-hand curb or edge of the roadway except under any of the
1. When overtaking and passing another bicycle or vehicle proceeding in the same direction.
2. When preparing for a left turn at an intersection or into a private road or driveway.
3. When reasonably necessary to avoid conditions (including, but not limited to, fixed
or moving objects, vehicles, bicycles, pedestrians, animals, surface hazards, or
substandard width lanes) that make it unsafe to continue along the right-hand curb
or edge, subject to the provisions of Section 21656. For purposes of this section,
a "substandard width lane" is a lane that is too narrow for a bicycle and a vehicle
to travel safely side by side within the lane.
4. When approaching a place where a right turn is authorized.
(b) Any person operating a bicycle upon a roadway of a highway, which highway carries
traffic in one direction only and has two or more marked traffic lanes, may ride as
near the left-hand curb or edge of that roadway as practicable.
A bicycle operated on a roadway, or the shoulder of a highway, shall be operated in
the same direction as vehicles are required to be driven upon the roadway.
1. No person shall ride, operate or use a bicycle, unicycle, skateboard, cart, wagon,
wheelchair, rollerskates, or any other device moved exclusively by human power, on
a sidewalk, bikeway or boardwalk in a willful or wanton disregard for the safety of
persons or property.
2. No person shall ride, operate or use a bicycle or unicycle on Ocean Front Walk
between Marine Street and Via Marina within the City of Los Angeles, except that
bicycle or unicycle riding shall be permitted along the bicycle path adjacent to
Ocean Front Walk between Marine Street and Washington Boulevard.