Common practice for creating software switchable power rails
You don't need a bridge circuit, just a single pass element between the power supply and the device.  This is usually a P channel FET if the supply voltage is 12 V or more.  That allows turning on the device by driving the FET gate 12 V below the power rail.  If the power voltage is enough for the full gate voltage to turn on the FET well, but less than the maximum allowed gate voltage, then this is as easy as a low side NPN pulling the gate low to turn the device on, and a resistor pulling the gate high to turn the device off.  Turning off doesn't need to be fast, so the resistor can be fairly high, like 10 k&Omega;, to avoid taking significant current when on.

If the power to the device is coming from a buck supply, then you only need to shut down the buck converter.  Some buck converter chips have a shutdown input that you could use directly.

Added

You now say that the power you want to switch is 5 V and that the control signal is 3.3 V.  This can be done with a "logic level" P channel FET.  Those turn on fully with 5 V or so gate drive.  Have the 3.3 V signal turn on a low side NPN.  That pulls the gate down, with a resistor pulling it up otherwise.

You also mention that this 5 V is regulated down from a 7 V or so battery.  This is exactly the case I was talking about where you get a buck converter that includes a shutdown input.  Many do.  At these low voltages, check out the offerings from Microchip.  Of course the usual suspects like TI and ST will have parts too.  Surely something suitable comes with a shutdown input.