Plain answer
Register on the portals where public tenders are posted, line up bonding and insurance before you need them, and learn the wage and prequalification rules for the owners you want to work for. The easiest start is usually as an electrical subcontractor to GCs who already bid public work: you learn the paperwork on their jobs before you carry the bid security yourself.
In the United States, federal opportunities are posted on SAM.gov, and states, cities, school boards and utilities run their own portals. In Canada, federal tenders are on CanadaBuys, provinces and municipalities have their own sites, and Québec public tenders are on SEAO.
Public jobs usually require bid security and often performance and payment bonds. Talk to a surety broker early: bonding capacity depends on your financial statements and takes time to build.
Owners set minimum insurance limits, and some require you to prequalify with financial and safety records before you can bid.
Many public jobs set the wages you must pay, such as prevailing wage on US federal work, fair-wage policies on some Canadian public work, and the construction collective agreements in Québec. They change your labor rate, so read them before you price.
Some places require trade bids to go through a bid depository, such as the BSDQ for many Québec projects. The instructions to bidders say whether one applies.
Ask GCs who bid public work to put you on their lists. You'll learn the forms, the bonds and the documentation on their jobs first.
One free bid check on every new account, no card required. Most checks come back in 5 to 15 minutes.