I may be a little off topic here as I'm not quite as versed on the "which side of river" which i want to hear more of what you all have to say for sure! a little off topic, sorry... I think it's based on wind direction in SOME cases with a SMART OLD BUCK. He may alter where he beds so he can get the best view with also the most dangerous areas having him being down-wind of. I sure don't know the technical answer to above and I can't read a deer's mind but I personally think they alter based on wind. Especially SMART OLD BUCKS which are a completely different animal IMO. They often bed in odd areas too.
Only thing I know for sure on my river system, Obviously if I have areas of nasty thick cover, usually they will be there. Or, say it's wide open (which mine isn't now!!!) - they will find a deadfall tree or brush pile to bed against.
Long discussion & could be another topic BUT I think what, where and why an OLD smart buck beds is going to be vastly different than say a 1-2 year old buck. Want to hear more responses on the inside/outside of rivers though. Interesting.