Rectifiers intended for 60 Hz applications are very slow, both slow to turn off and (interestingly) slow to turn on. They also have lots of capacitance.
If you're doing something slow, and working at very low impedance levels, then a 1N4007 could be the right part in this circuit. Personally if it was as slow as that I'd probably be wanting to use a Polyfuse and a Transzorb.
A diode has a nonzero conductance at zero bias--for an ideal diode, the zero-bias conductance is Is*kT/e, as you can easily verify by differentiating the diode equation. Bootstrapping will reduce the current, but won't reduce the noise. Pick something sensible--you've had several suggestions--and build something. Then tell us how it worked.
Cheers
Phil Hobbs