I can´t remember courting of women in the books at all. Actually most of the times when i think companionship, there seems to be more like spur of the moment events (Tarl and Talena in Tarsnman, the warrior and his slave in Assasins, Kamchack and Aphris in Nomads), or arranged things
Now it makes some sense also that love is not in place in a companionship. First of all, it is a civil contract: they get together for 12 months to produce a baby, then it might or might not be renewed (guess it depends on how good the sex and sharing of bed was) but if the mother is sent packing, the baby stays with daddy; she may not even see the baby again (mercenaries describes this in great length).
Second of course, how is somebody suppose to fall in love with a fully covered, fully veiled frigid, outspoken, arrrogant woman, instead of some hot, slutty and naked gorgeous slave? Clearly it seems that what drives a free companionship is either a commercial venture or some "fool" freeing a slave because he thinks she has earned the right to be free and is strong enough to produce good, strong babies to serve the homestone and continue the family lineage.
Incidentally, I think it is witness of gor where one sees what is the consequence of not accepting an offer to companionship by a suitor. In one of the chapters, when the tarnsmen of Treve raid Ar, and are being in pursuit by the patrols of Ar, a single tarnsman from Brundisium sneaks in, and captures a FW. The lady in question rejected his copanionship offer and now of course, she will be his, but serving him as the slave she had become.