How to deal with a drop ceiling that eats bass?

You need something solid and rigid to support bass. Dropped ceilings have 2 problems. One is the tiles, they are absorb in the upper frequencies and are transparent in lower frequencies. The second problem is the structure, it is not rigid. You have to fix both of these problems, and I doubt I can give you a "cheap" solution. It does depend greatly on the structure, but if there is a way to get rigidly supported drywall, that would be the preference. Mass loading is an idea. But it's unlikely you will acheive good rigidity at any lesser expense, since the metal channels for the dropped ceiling are not designed to support any significant mass.

My experience is that you live with it, or better yet get rid of it! Drop ceilings do what Rives said, and are an EASY source for noise and rattles. They suck up highs and some mid, and bass goes right through them.
How high is the SOLID ceiling above? What's it made of?
One solution might be to add some REFLECTION to places on the drop ceiling, so it will ad more diffusion and reflection. However, this depends on what else is going on in your room. If you have a carpet and lots of absorbtion around the room, your drop ceiling is DEFINTELY not helping your DEAD ROOM sound. Rooms will vary.
Good luck

Audiowill -

A speaker system that is directional in the bass might offer a practical solution. Dipoles come to mind, because that's the easiest way to make a directional bass system. A dipole will have a bass null in the plane of the driver, but would project bass forward and backwards. The very low amount of bass energy directed upwards towards the drop ceiling would minimize the ceiling's effect on bass performance.

Speakers with dipole bass systems include full-range planars such as Maggies, Quads, Sound Labs, and Martin Logan CLS's; as well as dynamic dipoles like the Gradient Revolution and the Audio Artistry line. I sell some of these, and I'd be glad to answer questions about any of them.

Best of luck to you!

Duke