Have you considered using a look-up table of sine vs angle values and DAC (digital-to-analog converter to produce the analog output? No weinbridge or RC shift oscillators needed. This reduces your parts count and creates an elegant, simplified, precise, digitally controlled oscillator. Simply cycle thru the look-up table at the desired rate to control frequency. You may want to add a low pass filter to smooth the DAC output to reduce harmonic distortion. A lookup table can be built for 1/4 of the cycle to reduce memory needed to store values for the first quadrant (\$0-90^{\circ}\$). Then use symmetry at \$90^{\circ}\$ to build the 2nd quadrant (\$90-180^{\circ}\$). Finally, repeat the 1st and 2nd quadrant with inversion to build the 3rd and 4th quadrants (\$180-360^{\circ}\$). This completes one cycle. Higher resolution is achieved with higher bit DAC. At the max. freq of 100Hz, you should have no problem finding a DAC to do the job. Build the look-up tables values by hand calcs (error prone) or use the first few terms of the Taylor series expansion of the sine function, for example:
$$\sin(x) = x-x^3/3!+x^5/5!-x^7/7!+...$$
The 1st 3 ot 4 terms should give a close approximation of the sine of the angle. \$n!\$ means n-factorial, e.g. \$5! = 5 \times 4 \times 3 \times 2 \times 1\$. So, you can actually program the equation in code and load values for each angle between 0 and 90 into memory.
http://en.wikipedia.org/wiki/Sine
For such a diode-stabilized WIEN oscillator you always have various options. One option you have shown with two equal resistors R22 in the parallel path. Here is my approach for dimensioning the circuit and for finding the output amplitude:
1.) For a safe start of oscillation we require (for example): (1+R22/R1)=3.2 with R22/R1=2.2
2.) During oscillations we have (Rd=statice diode resistance): [(R22+Rd)||R22]/R1=2
3.) From both equations we can eliminate R22 - and after some manipulations we get: Rd=1.98R1.
4.) Selecting R1=1kohm we have R22=2.2kohm and Rd=1.98kOhm
5.) Using a typical diode characteristic we find for Rd=19.8kohm a value of Vd=419mV and a current Id=0.02115mA.
6.) These values (Vd and Id) are the maximum values (ud,max and id,max) for the diode during the oscillation amplitude. The corresponding voltage across the resistor R22 (which is in series with the diodes) is R22*id,max=2.2*0.02115=0.0465V.
7.) Therefore the total voltage across the series connection (diodes-R22) is 0.0465+0.419=465.5mV. This value is identical to Vout*2/3.
8.) Result (oscillator amplitude): Vout,max=(3/2)*465.5=698.3mV( Simulation result: Vout,max=730 mV)
UPDATE/EDIT: Due to a simple calculation error I have corrected the above given values.
Best Answer
Any low-voltage, low-power incandescent bulb can be made to work. The trouble, in 2019, is finding them -- LED's just work so spectacularly better for making light from battery power, you'll need to dig around to find incandescent bulbs.
If you can find them, get some low-voltage (1.5 or 3V) "grain of wheat" bulbs.
If I were going to make a Wein bridge oscillator for production, I think I'd find an alternative to using a light bulb to set the gain. I'd probably use a separate amplitude-measuring stage followed by an electronically-variable resistor. For that I'd start with an analog multiplier, or perhaps a JFET or a switched-capacitor "resistor" operating well above my highest intended frequency. I might use a CdS photocell with an LED shining on it.