The official state gazette (BOE) has clarified rules on moped and motorcycle riders during Phase 1 of deescalation.
Gloves and either a full face helmet or helmet and face masks must be used if you have a passenger on the bike. (Normal motorcycle gloves are permitted).
Other travel guidelines permit people who live in the same household to be seated next to each other on public transport. If not cohabiting then an empty seat must distance you from other passengers.