Hi, Matty. You haven't said specifically what instrument you're using, so I can't give specific advice. But I can say for sure that Wheatstone bridges which only have two terminals for Rx aren't made to measure low resistance. You might be getting self-heating in one of the bridge's internal resistors, or if there's an active null, battery voltage may be affecting that. These are the first causes that come to mind.
Why don't you try using a 10 volt or so regulated power supply capable of cranking an amp or so, a 10 ohm or so resistor, and a voltmeter and ammeter. Connect the resistor in series with the power supply to give you an approximately 1 amp source. Put the ammeter in series with the circuit to measure current. Then put the solenoid in the circuit, and measure voltage across the solenoid. ` ` 10 ohm _ ` ___ / \\ ` .-|___|-----( A )-----. ` | \\_/ | ` 10V | | ` --- .-. ` - Rx | | ` | | | ` | '-' ` | | ` '---------------------' created by Andy=B4s ASCII-Circuit v1.24.140803 Beta
Even though this looks a little cheesy, it is in fact a true Kelvin connection, unlike your Wheatstone setup. This measurement will be as accurate as your ammeter. You don't need exactly 1 amp of current, because you can just do the math using Ohms Law to get the inferred resistance value:
R =3D V / I
Measure current each time you apply power -- it will change a little for every time you get a different Rx. Try to keep the application of power to the solenoid down to a few seconds or so if you can. That will reduce self heating, which is always a problem in measuring resistance of copper wire. Also look to ambient temperature, and prior heating of the solenoid coil from use. Make sure the coil is cool before you measure it.
Good luck Chris