Does it take some time to get the body ready for running and biking without socks. I would think that you would get some nasty blisters. Do you use body glide on your feet to prevent hot spots?
YUP... Use BG all the time on mine. Today was longggggg run day at 19 miles. I greased up with Body Glide and didn't suffer at all.
As for shorter runs, I started with 3 milers to aclimate my feet to sans socks. Then over a few weeks picked it up to 6. I do not run over 6 miles (10k) without socks. If it rains or the terrain is wet, my feet will blister beyond that point. Over 10K I use shorty Defeet cycling socks (they're thin & light). If over half marathon (13+ miles) I lube my feet with body glide or vaseline. In Marathons and Iron Distance triathlons, I also treat known hotspots with Liquid Bandaid. This puts a skin like coating on them but it's non-sticky so it doesn't hold dirt and you can't feel it in your shoe.
As for shoe type, I run Saucony Omni Grid 4's. They're a very comfortable shoe to run without socks in. Use speed laces to quicken your transition (T2).
OK... Cycling shoes... I ride Sidi T1s and Diadoras. I do not wear socks in rides or races under 60 miles. Over that, I treat my feet just as I mentioned in the run. HTH!