The arrival choice I would make
Choose by luggage and arrival time, not by pride.
- Use the bus when bags are light and you arrive with daylight.
- Use taxi or ride-hail when the hotel is tucked inside Old Town lanes.
Riga Airport sits close to the city, so the transfer is not the place to over-engineer the trip. A simple ride to your base keeps the first evening soft, especially if you are heading into Old Town's narrow streets or a Centrs hotel after dark.
If the hotel is near the edge of Old Town, check the exact drop-off point before you leave the airport. A car may not place you at the door, and a short cobbled walk with luggage feels very different after a late flight.