I pack bags in all sorts of ways, lenses go in the padded divider compartments however they fit best. Keep in mind that when for most backpacks, hard cases, and some other bag types, 'down' is relative. On my Lowepro Flipside packs, what is 'down' when loading them becomes the back side (away from my back) when being worn. Having said that, relative to when I'm loading I store shorter lenses with the front element/lens cap down (so they're sideways when wearing the pack or carrying/rolling the case, longer lenses lay on their sides with the lens cap pointing what will be down when the pack is worn. (Side note: longer 'sideways' lenses take up two 'spots' in the bag, that's one reason I went with the 70-300L over the physically longer 70-200/4L IS as a 'travel' telezoom.)
I've never had issues with caps popping off during transport. That includes my 24-70/2.8L II, but I should mention I have one of the earlier versions that came with the 'old' side-pinch cap instead of the 'new' center pinch caps. My only center-pinch caps are on my two EF-M lenses.
I pack the body with a lens attached, the mount is strong so there's no need to be concerned. Many bags are designed to be packed with a lens attached, sometimes the longest one.
Keep your empty bags zipped when not in use, clean them out occasionally (vacuum and wipe with a damp cloth).