One incentive for wealthy Romans to finance construction of aqueducts was, of course, glory. One's name would go up on the wall somewhere, and down in history, too.
However, there was more to aqueducts than just delivering water to cities for drinking, washing, cooking, and lavatory needs. For instance, hydraulic mining was all the rage in some places. One would run a spur from the existing aqueduct to indulge in a bit of ruina mortium, or hushing, to use water to bare up a gold or nickel vein.
Perhaps a prospector looking for funds might approach me, offering a contract and promising a sizable cut. Or I could hire someone to do some research to see if there were any areas that had growth potential, and the one obstacle was the lack of water.
Or, perhaps, the governor, or the Emperor himself, might send his agents to me, and I would promise, for a fee, to provide engineers, foremen, and slaves for an aqueduct project?
In other words: were there wealthy people in the Empire not personally involved in aqueduct construction who could invest in it on the chance they might turn a profit?