I read the California laws the other day, and they very specifically say that riding under the influence is illegal...
Bicycling Under Influence of Alcohol or Drugs. VC 21200.5
Provides that it is unlawful to ride a bicycle upon a street or highway while under the influence of an alcoholic beverage or drug or the combination of alcohol and a drug, punishable by a fine of up to $250. A person arrested may request a chemical test. If the person is under 21 but over 13 years of age, his or her driving privilege will be suspended for one year or delayed for one year once the person is eligible to drive.
However, it would appear to treat it differently than driving a car under the influence. From reading that, i'd say that for an adult over 21 its a $250 fine and no points or loss of license.
take care,
Jester