There are a lot of ways to navigate through the city with a bicycle. Heres a few maps to help.

Web maps

Ride the City - Shows bikeshare stations, bike routes, and bike shops.

OpenStreetMap Cycle Map- Shows off the bike related features in OpenStreetMap as well as some elevation topo lines.

Bike Mapper via 511- Mostly for routing with options favoring speed or least change in elevation.

Map My Ride Allows users to easily share their favorite bike routes and browse routes in particular areas.

Googley maps bike routing and is the standard bearer for reliably giving you a valid route.

Hill mapper to find the least steep direction from current location

Bay Area Bike Share Stations in SF From BABS.

Static Maps

San Francisco Bike and Walking Guide: In PDF form.

SF Bay Guardian Bike map from May 2011 - Looks like it was put together for bike to work day.

San Francisco Bicycle System- A map of bike routes modeled with a subway map style.

San Francisco MTA map - SFMTA street map with giant chevrons on streets from 2019.

Make a better one with the data provided by the SFMTA on their bike routes and share it here. The SF municipal goverment is even so excited about sharing data there are multiple datasets to draw from:

 https://data.sfgov.org/Transportation/SFMTA-BIKEWAY-NETWORK/9bqa-3n4q

https://data.sfgov.org/Transportation/SFMTA-Bicycle-Route-Network/q36i-k43q

Plus you could use data from the bike routes in OpenStreetMap or other sources.