Here is what I would do:
The 2x4's would attach to the joists with the bottom edges of each lined up. That creates two cleats on insides of the joist bay--I assume it is 16" from center of one joist to the other? Since "two by" lumber is really 1.5", you have 1.5" between the inside edges of your 2x joists and another 3" from the two 2x4's meaning your distance between is 11.5".
On top of the 2x4's I'd attach a 2x6 (or larger if appropriate) with it's face down. This creates the ceiling you'll attach the bag mount to--so this 2x6 is now recessed into the ceiling by about 3.5" (the width of the face of the 2x4's). You may need a few links of chain to add to the bag...
If you're paranoid and think that even with only an 11.5" span, the 2x6 isn't enough, you could stack & glue a second 2x6 on top of it, you'd essentially be creating a 4x6 up there.
Personally I'd attached everything together with a framing nailer, but I assume you don't have one, in that case I'd use some 2-1/2" wood screws, followed up by some 2-1/2" nails--the nails have greater shear strength, but the screws will hold everything in place tightly.
I think with this shelf inside the joist bay you'll be fine, but if you're up to Van Damm level you might start to twists the joists... in that that case I'd add blocking between the joists this shelf to attached to and their neighbors.
I hope this makes sense...