Unless otherwise stated in the code, elements of the LA Municipal Code are generally misdemeanors.
41.27(c) No person shall drink any malt, spirituous or vinous liquor containing more than one-half of one per cent of alcohol by volume, upon any street, sidewalk or parkway, park, playground, Los Angeles Memorial Coliseum, or in any railroad depot or bus station, or in any public place, or in any place open to the patronage of the public, which premises are not licensed for the consumption of such liquor on the premises.
So, by drinking the alcohol in public you committed a misdemeanor. And while misdemeanors may be released with a citation there does not appear to be any mandate in Los Angeles that they must be.
Has this been filed as a misdemeanor or an infraction? Is it being heard in criminal court or traffic court? If it is being pursued as a misdemeanor, then you could face up to 6 months in jail and a $1,000 fine (unlikely) and as such you should be eligible for publicly appointed counsel if you cannot afford an attorney. If filed as an infraction, then you are on your own and could only be subject to a fine (which, off the top of my head, would max. out at about $500).
Release on $20 bail is ... bizarre. I can only think that you did or said something to tick off the officer that contacted you. Most the time these matters would be released with a citation and not involve a custodial arrest.