What you suggest is possible, but you have to be aware of some gotchas. The biggest issue is for the transistor to not distort the measurement. You didn't give any accuracy requirements, but let's say it's a 10 bit A/D and you don't want the transistor to add more than 1 count of error. On the 3.3 V scale, one count of a 10 bit A/D is 3.2 mV. With the two resistors equal, the transistor therefore can't drop more than 6.5 mV. That completely rules out a bipolar transistor.
A P channel FET can do this. Again, if you want the transistor to not add more than .1% error it needs to be under 200 mΩ when the two resistors are equal, and half that in the worst case.
100 mΩ P channel FETs can be found, but N channel FETs are more plentiful and have better characteristics, especially at these low voltages. I would use a N channel low side switch instead:
The IRLML2502 is guaranteed to 80 mΩ max at only 2.5 V gate drive, so will add very little error. If much lower error is required, then you can measure the bottom of R2 in addition to the voltage divider and then the drop accross the switch can be accounted for in firmware.
You have now changed the question by saying you are really using a bridge circuit. This made sense when the measurement was to be displayed with a analog meter movement, but is unnecessary when using a modern microcontroller. With a normal microcontroller A/D you already have a bridge since the A/D result is ratiometric to the power supply range. In effect, the other side of the bridge is built into the micro. Using another external bridge and a second A/D input will only add error. If you're fine with .1% voltage accuracy coming out of the divider, then just use the circuit above.
Some microcontrollers have a separate negative A/D voltage reference line. This is called Vref- on Microchip PIC line, for example. You could drive Vref- from the bottom of R2 to ignore the voltage accross Q1. However, check the valid range of the the Vref- pin. This may not be allowed to go as high as Vdd. This is actually one case where you may be able to use the absolute maximum rating instead of the operating values. When the sensor circuit is off, you only care that the A/D not be damaged, not that it work correctly. Of course if you are using the A/D for other things this scheme won't work.
More on bridges:
It has been suggested that a "bridge" circuit is better in this case and would cancel out any voltage dropped by Q1 in the circuit above. This is not the case, at least not with my interpretation of "bridge" circuit. Here is how I think the bridge is intended to be connected:
R1 is the variable resistance sensor being measured. R2, R3, and R4 are fixed resistors with known values. SW1 is the switch used to turn this circuit off when not in use to conserve power. When a measurement is being taken, SW1 is closed. In this schematic, SW1 is assumed to be a perfect switch with R5 shown separately to represent its on resistance.
The point of a bridge circuit is to provide a differential voltage between V1 and V2. This was useful in old analog meters when the meter required significant current and could be directly connected between V1 and V2. Note that the voltage V1-V2 is still proportional to Vdd. This circuit is not independent of Vdd, and therefore not independent of apparent error in the supply voltage caused by the current thru R5. Bridge circuits are independent of Vdd in only one case, and that is when V1-V2 is zero. This is why old analog meters that used bridge circuits combined them with a precision calibrated variable R3. You wouldn't use the measurement of V1-V2 displayed on the meter as a direct measurement, but rather as feedback of setting R3 such that V1-V2 was zero. In that singular case, Vdd then does not matter, and neither does the impedance of the meter between V1 and V2.
What we have here today with microcontroller A/D inputs is a totally different case. These A/Ds are not set up for differential measurement, and we don't have a calibrated reliable way of varying R3 anyway. However, we can make fairly accurate voltage measurements realtive to the GND to Vdd range.
If R5 were 0, then the voltage at V1 would a ratio of Vdd dependent only on R1. Since both the sensor circuit and the A/D in the microcontroller produce and measure the voltage relative to the GND to Vdd range, the exact value of that range cancels out.
The only problem is when R5 is non-zero and unknown over some range. This adds a unknown error to V1 even when it is considered relative to the Vdd range. In effect the sensor is producing a voltage a fixed fraction of the Vlow to Vdd range, while the micro is measuring it as a fixed fraction of GND to Vdd. The simplest way to deal with this is to guarantee that Vlow is a sufficiently small fraction of Vdd so that this error can be ignored.
The suggestion to use a bridge circuit is apparently so that measuring both V1 and V2 allows this error to be cancelled out. If R3 and R4 are well known, then the V2 is a direct function of Vlow, but attenuated by the R4,R3 divider. With high precision, V2 could be measured, Vlow inferred, and the result used to correct the V1 reading. However, there is no advantage to the R4,R3 divider. If you need to correct for Vlow, it is best to measure it directly. In no case is measuring V2 better than measuring Vlow directly. Since we are better off measuring Vlow and therefore have no need for V2, there is no point in producing V2. R3 and R4 can therefore be eliminated, leaving nothing that could be called a "bridge" circuit.