Q: If I don't wanna do this, will I just have to IMAGINE the bass note  while playing non-root harmony in left hand, solo in right hand?
A: oh i see. you're trying to play melody things with your right hand, while also somehow accompanying yourself with your left hand. and i think, reading between the lines, you have no bass player. in that case, what you are doing requires 3 hands. if it were me, whenever i'm on a keyboard by myself, it's always bass in the left hand, and pretty much everything else with right hand, and, of course, my voice. If you are not allowed to use your voice, then i'd say just do bass notes with left hand and melody stuff with right. eventually it will become instinctive to start also throwing chords and harmonies in, with the right hand also. for example, if you play melody note E, and the chord is C, you might play E and C with the right hand. there's actually 1000 different ways to use the piano, and it's different depending on how many other players you have with you, and whether or not you are singing