Mass helps- blowing cellulose insulation between the joists in that area will make a difference for noise generated completely within the bathroom, but you likely have other issues with drain noise as well (especially if you have plastic drain plumbing.) There again, if you can pack the plumbing chase full of cellulose it'll deaden it quite a bit. This can be often done as a retrofit with one easily patchable 1.25" hole per joist bay. Without internal blocking the insulation will spread beyond the exact perimeter you're looking for, but so be it... (cellulose in layers that thick add significant thermal mass to the building too, a secondary benefit.) Basically, drill the hole near the most interior portion of the section of joist bay you're trying to treat blow toward the exterior wall untill it can't get any more in- it'll be mostly full, with a density somewhere around 2lbs/ft^3. (If the gypsum board is thick or it's plaster on lath you can probably "dense-pack" it to 3-3.5lbs/ft^3 with a 2" hole, inserting a 1-1.25" hose to the end and pulling it back 6-8" every time the blower starts to back up. It doesn't have to as perfect a job as when using for thermal insulation- it could be a DIY weekend project for most reaonably handy people, using a box-store rental blower. (Be prepared to clean up some non-toxic dust- mostly borate fire-retardent mixed in with the cellulose.)

If the cheap rental blower only has an open-ended 2" hose you may need to fabricate a reducer nozzle from plumbing fittings (copper preferred). If the end piece is a 45 degree elbow you can usually get good enough aim to blow it directly horizontal. Full 90 degree ells tend to clog, but if you saw it off a bit making it something of a spoon, that gives pretty good directional control too (but a wider spread to the spray.) The fittings can be heavily duct-taped together (and to the 2" hose) as long as they dry-fit reasonably tightly. Soldered/hose-clamped is better though.

Some cellulose insulation contractors would be willing to take on the job at a reasonable price, but be very specific about what you want. It'll be difficult to assess accuratly ahead of time just how much material it will take but the stuff's pretty cheap. The drilling & probing time can be as much as half the project.

Beyond that, a second layer of gypsum board glued with sound deadening adhesive (see: http://www.greengluecompany.com/ ) adds both more mass and several dB better isolation. This would likely be more work than a cellulose fill since it involves complete refinishing of the ceiling and possibly the wall adjacent to the plumbing chase.

thanks Dana1. Very complete answer. This is along the lines of what I visualized doing. Fortunately I took pics as the house was being built so kind of know what is inside the walls and joists. Another option I thought of was to cut sections in the ceiling and possibly walls and stuff in batts.

Batts help some, but they're lower density, and harder to fill in completely.  Any blown insulation will work better, fill in better. Cellulose is higher density than blown fiberglass or rock wool (unless you dense-pack them), and it's cheap & available at box stores- probably the best choice here.   You can get slightly better R-value in cavity blows out of fiberglass than cellulose for roughly half the weight, but that's not our goal, eh? Here want to maximize density, not R-value.

Blowing insulation isn't rocket science. A dozen patched holes will be a lot easier than hacking stuffing & replacing whole sections of gypsum.  If you want to learn all about it, (more than you needed/wanted to know), a guy named Rick Karg has tons of web-published tricks of the trade- google [ Karg cellulose ] and you'll get hundreds of hits, many of which are pictorial instructional type stuff.  Some box-stores will give you a weekend of free blower rental with $100 of material.  That would be about 10 bags, 250lbs, which should do it for the joists of the square footage of a bathroom, unless it's a real palace. You can usually return any unopened bags. The drilling & blowning would be about a long afternoons-worth. Figure for yourself what the patching & painting would take.