Cape Town isn't the most bicycle-friendly city in the world - you won't find many bicycle-only lanes, and other road users are often bemoaned for not paying proper attention to cyclists (and motor-cyclists for that matter).
But, that said, Cape Town is actually a very cycle-able city on weekends and public holidays when traffic isn't so heavy. One sees a great deal more bicycling the city streets than one would from a bus or car. This time of the year is the perfect time to cycle the city - the sun isn't nearly as hot as it is in summer and the wind tends not to blow much at all.
Take a look at one of the bicycle-hire companies - most of them even offer guided tours of the city, vineyards, or MTB trails. Take a look at RentABicycle, Bike & Saddle, and AWOL Tours.