It sounds exactly like the motor I have on my Quorn, an SD15 I think.
If you have a multimeter check continuity between black and each white. If one of the whites is open circuit the motor is probably scrap. White windings should have the same resistance.
If the windings are both OK the wiring is as Clive suggests. Depending on which cap/white junction you connect to the motor should run one way or t’other. If not the cap it probably shot. A single pole changeover switch can then be used to select forward or reverse.
If it needs a new cap the value on mine is 8.4 uF 440 V. Get a cap designed for motor use. They are pretty cheap.
https://uk.rs-online.com/web/p/film-capacitors/3779074