Bimetalism is a bad idea because it implies a fixed ratio between one and the other.
A "Gold dollar" is an equally bad idea.
The idea that a limited supply of money would cause a depression is false. In 1913 the federal reserve act created a source of essentially unlimited credit, that's why the '20s roared, and why we had the great depression. A limited supply of money worked just fine for centuries, it only took 16 years for the FED to cause a depression by providing unlimited credit in a finite money environment.
Blaming the depression on a finite money supply is like blaming a car crash on the telephone pole.
It isn't about gold, it's about an alternative to debt instruments as legal tender in payment of debts, which is quite possibly the worst idea in the history of the world.
The utility of gold as money isn't dependent on intrinsic value.
The intrinsic value of gold is its utility as money.
The solution to the monetary question isn't a "gold standard" a bimetal standard, paper standard, oil standard, or any other kind of standard.
The solution is simply to eliminate legal tender from the equation entirely, write contracts in any means of exchange you choose, and whatever the most liquid asset is will rise to the top and be money on its own.
In the past, absent coercion, it's always been metals, maybe someday something else will work better. It really doesn't matter, it's the force applied by legal tender laws, particularly when that law mandates use of government debt instruments, that is the source of the problem, and of the growth of federal government power in the last century.
Real money doesn't require force of law to make it good.