In the tune's usual key of Bb, the chords to the bridge are:
|| D7 | D7 | G7 | G7 |
| C7 | C7 | F7 | F7 ||
However, these are not the chords that we see in the "original" sheet music, or in charts that are modeled on the "original" changes. Below is the bridge in what I think was its original form (I've had this sheet lying around for quite a while; I copied it from a Gershwin collection). Click to enlarge.
The chord symbols, taken by themselves, leave a false impression. As shown, they are not functional, but rather just an attempt to represent the notes in the piano arrangement. If a guitar plays the symbols while a piano plays the arrangement, it will sound OK. However, if you follow only the chord symbols, the harmony will sound fragmented and discontinuous - unless you are so extraordinarily clever that you can recreate the piano arrangement from the symbols!
The real gist of the harmony is in the left hand bass notes, which indicate:
| D7 | D7 | G7 | G7 |
| C7 | C7 | Gb7 | F7 ||
The many additional chord symbols attempt to represent the mostly-chromatic inner voices in the right hand, particularly the line that starts by ascending from F# in the first bar of the bridge, in the chart above (lyrics: "Old Man Trouble...").
Here's a priceless clip of George Gershwin playing "I Got Rhythm" in 1931. You can clearly hear the chromatic line in the bridge, although he alters it a bit in the third and fourth bars, continuing the line upwards. In this clip, he plays the tune first in Db, goes briefly to D, and finishes in Gb.
I found a few more printed "lead sheet" versions that seem to have been derived from the sheet music, showing similar chord symbols for the bridge:
Tune-Dex fakebook (c. 1949):
| D7 C | Ddim D7 | G D+5 | Dm G7 |
| C7 Bb | Cdim C9 | Gb7 | C7 with Gb ||
Dick Hyman's Professional Chord Changes and Substitutions for 100 Tunes Every Musician Should Know :
| D7 Am7/E | Fdim F#m7b5 | G D7+5 | Dm7/G G7 |
| C7 Gm7/D | Ebdim Em7b5 | Gb7b5 | F7 ||
Just Gershwin Real Book :
| D7 C/E | Fdim D7/F# | G7 F/A | Bbdim7 G7/B |
| C7 Bb/D | Ebdim C/E | F7 | F7 ||
For comparison, here is the progression from the "original" sheet music, above:
| D7 Am7 | Fm6 D7 | G D+ | Dm G7 |
| C7 Gm7 | Ebm6 C9 | C7b5 | F7 C7 F7 ||
All of these seem to be trying to suggest the chromatic inner voice leading in the original piano arrangement, or some similar line.
Jazz players don't generally pay much attention to this line when playing tunes based on "Rhythm changes." Typically, they'll either just follow the basic chain of dominants, or use that as a basis for an elaborated progression (a couple of examples are shown here).
The pared-down approach seems to have started pretty early. Here's a Red Nichols version from 1930:
There's some interesting material in this Wikipedia article, including the fact that "I Got Rhythm" was actually written in 1928, as a slow song for the musical "Treasure Girl," but was re-used two years later in a faster setting, for "Girl Crazy."
The basic harmonic pattern of the "Rhythm" bridge was used by George Gershwin for the bridges in several more of his songs (I found these in the Just Gershwin Real Book); the first two definitely predate "I Got Rhythm":
Hang On to Me (1924)
Sweet and Lowdown (1925)
Feeling I'm Falling (1928)
Boy! What Love Has Done to Me (1930)
But this bridge idea wasn't necessarily original with Gershwin. The same harmony occurs in the bridge of "Five Foot Two, Eyes of Blue." That song was copyrighted in 1925, but according to Wikipedia, may have been composed in 1914.
Aside from the fact that the "chain of dominants" progression is about as old as European classical harmony, I have to wonder if there isn't an even earlier example in American popular song, operetta, or ragtime. Please let me know if you run across one. To qualify, it has to be an 8-bar bridge in a 32- or 34-bar form, starting on the III dominant, then moving around the circle of fourths, 2 bars per change.
