What does "short" mean? I'm asking because investing in camping gear probably costs more than a few nights at motels. If you just want to see if you like it, you could either borrow camping gear or stay in motels, and then invest if you decide you are sure you want to continue.
Apart from that - yeah, 4 person tent is too big, if you are going to do most of your touring alone but a little with the wife, you will probably want a 2 person tent for yourself alone and a 2 or 3 person tent for the both of you. Weight matters. if the wife-camping part is just car camping, you could get a separate 4-person cheap tent for that, and a nice/light 2 person tent for your bike touring. do not carry a 4 person tent with you for many days on tour because of a few nights you may or may not need that tent in the future. Penny-wise and (literally) pound-foolish.
REI-Outlet is a good source of camping gear. And see what your friends would be willing to loan you. I loan my touring and camping and bike gear pretty regularly to local friends, and have borrowed stuff too.