Whether I would rent a car or not depends on various factors:
1. Do I need the car after Bonassola? For sure you won’t need it on the Ligurian coast if you plan to visit the Cinque Terre or similar. The train is better.
2. Will I be jet lagged after a long flight?
If decide to rent I car you will need at least half hour for the paperwork and pick up at the airport. There is no way you can drive from BGY to Bonassola in 3 hours, not even if you rent a Ferrari and you are a formula 1 driver. Plan on almost 4 hours, plus pit stops for biological needs. The drive is almost all freeway but you need to go through the Milan tangenziale (beltway), and if it’s around commute time you can forget about making in 4 hours.
I don’t know at what time your plane lands, but the most convenient way, if you don’t absolutely need a car for portions of your trip after Bonassola, would be a taxi from BGY airport to the station in Bergamo (10 to 15 min ride), then train with two changes, one at Milano Centrale and one probably at Sestri Levante.
I don’t know if you would save time with a taxi to Milano Centrale. That will depend also on the traffic. The cost will be higher as the taxi fare to Milan would be 120€. There is no Uber or Bolt driven by regular folks in Italy (prohibited by law). Uber provides only the Uber Black or the Uber Van service in Italy, which are black limo services driven by licensed limo drivers and cost more than the regular taxi.
