If you stop taking your meds, how long will it take for your body to reject a donated heart?

Usually within a day. Most antirejection medicines must be taken once or twice a day. Once stopped the drug levels will usually dip below the therapeutic threshold within a day and the rejection process will begin. The speed of progression and the severity is different for everyone and is dependent on how tolerant the patient has become to the transplanted organ.
Fasterthan you think. It would depend on how robust your immune system is and how rapidly one would metabolize (remove) the remaining anti-rejeciton drugs from their body. It is not something an organ transplant recipient should experiment with.