That won't be able to drive '100mA into 50 ohms'
Be aware if the battery is a PP3 it will have only a short life driving 100mA; or were you proposing to use a stack of AA cells or bigger?
I'm sure we can come up with a circuit.
If I understand correctly, you want a reversible current source 0-100mA from a 9V battery. The polarity changing can be done with a DPDT switch between the load and the current source (or any number of other methods), and the current source can be accomplished using an opamp current source with voltage reference and shunt resistor (similar to attached image - can make use of a PNP or PFET [& swap opamp inputs] to ease battery voltage requirement).
Regarding battery life, an alkaline 9V battery should last in excess of 3 hours at 100mA drain and still be above the required 5V (100mA into 50ohms). https://www.powerstream.com/9V-Alkaline-tests.htm
That will give you about 10 hours @ 50 mA: https://www.electro-tech-online.com/custompdfs/2012/08/522.pdf Make sure you have enough compliance, because as the battery voltage drops, the current may too. Remember to take into account the drops inherent in the OP amp etc.