I'd put it inside the backpack, in a waterproof stuff sack, inside a pack liner, because I carry down quilts and don't like putting $500 in gear on the outside of the pack where a branch or random trip and fall into a stream will totally unmake my day. Sleeping pads, the tarp, the hammock, those I've put in pack outer pockets or strapped on the bottom or down the side.
"In the beginner's mind there are many possibilities. In the expert's mind there are few." Shunryu Suzuki
What kind of pack are you using? From the way you describe it, it almost sounds like you're using an external frame pack. If so, you're approaching it right; you'll definitely want to use a stuff sack for the bag, though.
If it's an internal frame pack, the sleeping bag should go inside, usually at the bottom of the pack. A stuff sack isn't strictly necessary (I just stuff mine in loose, so it fills all the space) - but if you use one, you might want to use a fairly large one, so you can mold it into the bottom of the pack, too.
Back when I used an outer frame pack I'd lash it onto the top or bottom of the pack horizontally. It would catch on brush and get wet when it rained. (It's a good idea to use a waterproof stuffsack in this situation.) Now I have an internal frame pack, and the sleeping bag packs inside where it's protected.
If you can't get it to fit inside, there are a few things you can try: 1) Use a pack liner and don't bother with a stuffsack for the sleeping bag; insted, put it loosely on bottom and put the rest of the gear on top. The gear will compress the bag a little and the bag will fill some of the empty spaces. 2) You can put the sleeping bag in a compression stuffsack. This will compact it as much as it can, and it should fit. You wouldn't want to keep it compressed like this longer than you have to, though, otherwise the bag will lose some of its fluff & get cold.
If you are using an external frame pack, put your sleeping bag in it's stuff sack and then in a heavy duty garbage bag or trash compactor bag. Push the air out, twist the top closed, double it over and tie with a twist tie. As long as you aren't pushing though heavy brush that should keep you bag dry and safe.
If I wouldn't eat it at home, why would I want to eat it on the trail?
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