Ok, let's approach this from the beginning, so to say.
A smoothing cap sitting between a source and a load is itself a load and a source at different times of the operating cycle. If it wasn't, nothing useful would happen. So part of the source cycle the "true" source is supplying the "true" load, as well as charging the cap. The rest of the source cycle the cap is supplying the "true" load. The load cycle for its part affects the details of this charge/discharge cycle.
To estimate/calculate the ripple, a number of things must be known:
1. What kind of source is supplying the DC rail of your bridge. You say the rail voltage is btw 10 and 18 V but not from where. For the sake of argument i assume an iron transformer secondary with a full bridge rectifier. That means your smoothing caps sitting across the rail will charge rather spiky.
2. There are 2 kinds of ripple, a) voltage ripple and b) current ripple. Both will be influenced by the capacitance of the smoothing caps. The capacitance you have arrived at is very low for a medium current PSU. A more plausible value would be several 1000 uF. But that depends entirely on the nature of the supply. I am assuming point 1 above.
Wait a minute. Is this the same project that you said would be fed from a battery? In that case you won't need much of a smoothing cap at all - the battery is one huge cap in itself. There is nothing you can do about the motor coil inductances, but they are not a problem. In fact the inductance limits the di/dt and that way also ripple currents and voltages. If you have very long feeder cables then a cap in a strategic place might do some good, but please throw away the pitiful piece of mouseshit and shop in this department instead:
http://www.digikey.com/scripts/dksearch/dksus.dll?FV=fff40002%2Cfff80009%2Cfffc0152%2Cfffc01ef&vendor=0&mnonly=0&newproducts=0&ptm=0&fid=0&quantity=0&PV16=11813.
These are caps for grown-ups and they are what you want in a PSU. The SMD cap while from a quality mfg that i use myself, just isn't in this league. I am not saying you must have one of these caps in the circuit, but you might want one - depends on the details of the circuit and app.