The sorts of voters likely to vote in initiatives generally tend to be skew towards those distrustful of government. A bicameral legislature by its very nature makes passing laws more difficult, which is exactly what those who distrust government should favor.
Turn-out would be pretty good if it was a normal initiative synced with the general election. California recently changed its law so there's no more initiatives in primaries for that reason.
I'd definitely be curious to see how it played out; I don't think it's been tried in any state since
Reynolds v. Sims changed the base of representation for all state senates. Especially in a state where Democrats have such big super-majorities. Even some conservatives could support abolition if they see it as working against them (another chamber they have to win). Kind of like how the Oklahoma state senate recently passed the National Popular Vote Interstate Compact.