Our physics master taught us that we can't use meterbridge to measure low resistance but he didn't give a valid reason for that.
A Wheatstone bridge works best (smallest error) when the resistors are all about equal. Having two small resistors in series on one side of the bridge will result in a lot of current (maybe more than the supply can handle), heating, and errors in the measurement. And because you're measuring the voltage across the same contact that carries the current, you will be more sensitive to contact resistance (compare this with the 4 point Kelvin probe arrangement that circumvents the problem and is more suited for low impedance measurements). Furthermore, the slightest imbalance in the bridge will send a large current through the galvanometer - which might well break it.
On the other hand, when resistance gets very high, the currents that would flow if the bridge was unbalanced become very small, and this may make them hard to detect (it depends a bit on the make and model of the device you use to detect the imbalance). Here, for example, is the calculation of the current that flows when you have two resistors of resistance R in series, with 10 V across the bridge, and you offset the jockey by 5%. I will assume that the resistance of the wire is lower (maybe 10 kOhm) so it doesn't really come into play.
We see then that there are unequal voltages across the two resistors; with the jockey 5% off center, the voltages will be 5.5 V and 4.5 V respectively. There is a net current of (5.5 - 4.5)V / (1 MOhm) = 1 uA that flows through the galvanometer.
That's not a ridiculous small current - but it is already near the limit of what ordinary mechanical (coil and needle) devices can measure. So as resistance increases, your ability to measure it accurately with a bridge decreases.
Is this part of a homework problem?
Low resistance - think about how you would connect the resistors to the bridge.
High resistance - think about how you note when the bridge is balanced.
The answer to your question is in all three Physics textbooks that I have opened as well as a couple of webpages.