There are up to 4 valves.
Your bypass is either a 1,2 or 3 valve system, IF it is a 1 valve then there *IS* a check valve on the outlet of the tank (may also be one on the inlet but let's skip that for now) if it is a 2 or 3 valve system there MAY still be such a check valve.
in the 3 valve system.. Your plumbing makes a Capitol letter H, lying on it's side.. For winter use the center valve (on the cross bar of the H) is open and the two that go to the tank,,,closed.. For summer it is the other way around.
A bypass needs THREE valves.
On the 2 valve ssystem they use what are called "3 way valves" so when both valves are turned to BYPASS, they make the 3rd valve between them.
On a one valve bypass the valve, being a 3 way, replaces the COLD and Bypass valves, but the HOT valve is replaced with a check valve to keep winterizing solution (Pink stuff) from back flowing into the hot tank.
THIS valve is often present even if not needed.
It gets gummed up with mineral deposits and sticks closed, The solutions are as follows
1: Replace it (Often impossible to remove)
2: Gut it, PUll the guts out using needle nose pliers and hook direct.
3, if you have the flexibility... Gut it and install a 2nd check valve or...
Gut it and replace the "T" fitting with a 3 way valve (turn it to a 2 valve system) or you can put a simple quarter turn valve in the line between the "T" and the water heater. (Cheaper than a 3 way)
Damon gave me the best system (3 valve) in my opinion