OK, here's the circuit I came up with. You might need to change some values. For low offset voltage, the diodes in the bridge need to be matched. You can probably find a better op amp. It just needs to have low input bias current, high bandwidth, and high slew rate. I picked this one because it was in my library.
I'm including the .ASC file in case anyone wants to simulate it in LTspice.
Here are the models for the diodes and the transistors.
Code:
*
.SUBCKT 1ps70sb10 1 3
* The Resistor R1 does not reflect
* a physical device. Instead it
* improves modeling in the reverse
* mode of operation.
*
R1 1 3 3.6E+07
D1 1 3 1ps70sb10
*
.MODEL 1ps70sb10 D(
+ IS = 2.117E-07
+ N = 1.016
+ BV = 36
+ IBV = 1.196E-06
+ RS = 2.637
+ CJO = 1.114E-11
+ VJ = 0.2013
+ M = 0.3868
+ FC = 0
+ TT = 0
+ EG = 0.69
+ XTI = 2)