There is no free parking in the city centre, expect for on bank holiday and weekends (Saturday after 5pm). Even then you need to be sure to park in the the right places (boligsoneparkering) and obey all other regulations. Fines are frequent and high, so chance it at your own risk…

The safest option is parking garages.

Klostergarasjen is the closest to the apartment and cost 200Nok per 24hours.

Bygarasjen is a 10 min walk and cost 150Nok per 24 hours.

https://bergenparkering.no/priser/rates-and-pricing-information/