If you know the public law number, you can find the bill number in the Statutes at Large. (KF50, 4th Floor Stacks). To obtain the bill numbers for early Congresses (1st to 57th, 1789 - 1903), consult the Legislative Reference Checklist (KF49 L43 1982, Reference Desk).
The first bill in the House of Representatives in each Congress is identified as H.R. 1, and each subsequent House bill is numbered sequentially. Likewise, the first bill introduced in the Senate is identified as S. 1, and each subsequent Senate bill is numbered sequentially.
Bills on Internet Subscription Databases Available at UC Law SF:
ProQuest Congressional (access: restricted to UC Law SF students, faculty, and staff)
indexes bills from the 1st Congress to the most recent Congress, and provides full-text and status of bills from the 101st Congress (1989) to present.
ProQuest Legislative Insight (access: restricted to UC Law SF students, faculty, and staff)
contains bills from 1970 to present; by the end of 2012, the database will contain bills from 1929.
Lexis (access: restricted to UC Law SF students, faculty, and staff)
Offers full-text of bills introduced in the House and Senate since the 101st Congress, and tracking of congressional bills for the same time period. From the main Lexis search page, select "Legislation and Politics," select the subcategory "US Congress," then select the subcategory "Full Text of Bills - Historical.
Westlaw (access: restricted to UC Law SF students, faculty, and staff)
Offers full-text of bills from the 104th Congress to date in the following database: CONG-BILLTXT-ALL.
Bill Tracking for the current session is available in the database US-BILLTRK and for older bills (from 2005) in BILLTRK-OLD. (Note: BILLTRK-OLD combines federal bills with state bills).
Internet: Government Websites
Congress.gov
Includes the full-text of bills from the 93rd Congress (1973) to the present.
govinfo
Includes the full-text of bills from the 103rd Congress (1993) to the present. Replaced FDsys in 2018.
Library of Congress
House Bills and Resolutions (from the 6th to the 42nd Congress (1799 to 1873)), Senate Bills and Resolutions (from the 16th to 42nd Congress (1819 to 1873)), and Senate Joint Resolutions (from the 18th to the 42nd Congress (1823 to 1873)).
Bills on Microfiche
UC Law SF: Federal bills are available on microfiche from the 96th Congress (1979) to the 110th Congress (2008). The bills are in Micrographics. See a Reference Librarian if you need help.
San Francisco Public Library: Bills from the 75th Congress (1937) to date on microfiche, located on the 5th Floor.
UC Berkeley Law Library: Bills for the 1st-24th and 37th-55th Congresses available on microfilm.
Stanford University (Green Library): Bills from the 1st to the 100th Congress (1789-1988) on microfiche.