Everything said is true (except I'm not getting the robotics comments). My 2 cents:
I know putting a 1 ohm resistor between the cathode and ground gives me exact millivolts.
All voltage can be expressed in mV. E.g.: 1V = 1000mV. I.e., there nothing magical about the expression of a value in mV, mA, etc. E.g., the same capacitor value can be expressed in pF, nF, uF or mF, or F. The point is that to understand amp circuits, free of mental confusion, it's important to get comfortable with the placement of the decimal point, and how this affects proper nomenclature. Failure, refusal or procrastination in learning this will keep your head spinning.
Also, whether a value in a schematic is expressed in mV or V; nF or uF; etc. is a matter of convention. But, the formula's -- Ohm's Law, and the Power Formula, etc. -- require the values to be stated in Volts, Amps, Ohms and Farads. I.e., if you use mV and mA in Ohm's law, you'll get the right "absolute" answer, but the decimal point will be in the wrong place.
When you look at various biasing settings for tubes, it's in current, mA's. So, it's said the 1 ohm resistor reading is mV but it's really mA'a, cause it's across a 1 ohm resistor..? Can't wrap my head around this, how does volts change to current...?
You have to learn & get comfort with Ohm's Law or be doomed to mystery & confusion. Voltage Drop = Resistance x Current. Hence: Current = Voltage Drop / Resistance.
If me make Resistance 1 Ohm, then Current = Voltage Drop / 1. I.e., Current = Voltage Drop!!!
If a voltmeter tells us that 33mV are dropped across the 1 Ohm bias sense resistor, we now know that = 33mA.
There is no magic in the use of a 1 Ohm resistor. You could use ANY small (so as not to disturb the overall cathode resistance) value for the bias sense resistor, say 2.7 Ohms. Then, Current = Voltage Drop / 2.7. But it's quick & easy to use a 1 Ohm resistor and skip the arithmetic.
OTOH, a 10 Ohm 1/2W bias sense resistor could be used. This shifts the meter reading by 1 decimal place. The advantage is that the resistor serves double duty as a "fuse" to protect the power tube. This is often seen in vintage amplifiers, but has fallen into disuse. I mention it to illustrate the decimal point issue. (It's almost as easy to divide by ten as to divide by one.)