I lot of people do indeed say that the plural of "bar" is "bar", and I have heard it repeated for the last 30 years, but I fail to see why this should be so. Apart from that, many people working in fields where they use the term also use the plural "bars".

Now were "bar" an abbreviation, then yes, the plural would be invariable. Cf. 10 volts but 10 V, 320 megapascals but 320 MPa, 32 pounds per square inch but 32 psi, 10 minutes but 10 min, 30 seconds but 30 sec, etc.

"bar" is not an abbreviation, however, but a word in its own right, though admittedly it has been shortened from the Greek word "baros" = "weight" (of air) that gives us "barytes/barite".