I don't know the specific laws in CA for riding in a crosswalk, but here in AZ (both CA and AZ are in the USA) it is actually ambiguous. While on a bicycle, you become not a pedestrian, which in AZ means that you aren't afforded the legal protections of a pedestrian, which means that in cases like yours there is no legal recourse.
However, riding a bicycle on a sidewalk here in AZ is illegal, and for good reason.
Section 275 of the CA motor vehicle code states that the crosswalk is an extension of the sidewalk, so if riding on the sidewalk is legal where you live, then you had the right of way.
After looking around, it appears that CA has a hodge podge of local ordinances pertaining to the legality of riding on the sidewalk.
Culver city ordinance §7.04.250 RIDING ON SIDEWALKS. states
A. No person shall ride a bicycle upon a sidewalk within any
business district or upon the sidewalk adjacent to any public school
building, church, recreation center or playground or upon a walkway
specifically designated by resolution of the City Council as closed to
all vehicular or bicycle traffic. B. Whenever any person is riding a
bicycle upon a sidewalk such person shall yield the right-of-way to
any pedestrian and when overtaking and passing a pedestrian, after
giving an audible signal, shall at all times pass to the left of such
while the ordinance for LA county, §15.76.080 Driving or riding vehicles on sidewalk. states
A person shall not operate any bicycle or any vehicle or ride any
animal on any sidewalk or parkway except at a permanent or temporary
driveway or at specific locations thereon where the commissioner finds
that such locations are suitable for, and has placed appropriate signs
and/or markings permitting such operation or riding.
and for the City of Los Angeles SEC. 56.15. BICYCLE RIDING – SIDEWALKS. states
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. (Amended by Ord. No. 166,189, Eff. 10/7/90.)
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. (Amended by Ord. No. 153,474,
No person shall operate on a beach bicycle path, or on an area of a beach which is set aside for bicycle or unicycle use, any bicycle
or tricycle which provides for side-by-side seating thereon or which
has affixed thereto any attachment or appendage which protrudes from
the side of the bicycle or tricycle and is used or designed to carry
another person or persons thereon.
For the purposes of this section motorized bicycles as defined by Section 406 of the California Vehicle Code shall be included within
the terms “motor vehicle” as defined in Section 415 of the Vehicle
Code and as used in Section 21663 of the Vehicle Code.
So it appears that it depends...