I recently maxed out points in archery including the Ranger perk but then later decided I really didn't need to have any in it so I reset my archery points.

I then put some back into archery but left the Ranger perk empty, continued playing Skyrim for a bit, came in contact with a bad guy that I felt like filling up with arrows, pulled out the bow and sure enough my character was still moving fast with the bow drawn just like he would if he still had the Ranger perk.

It's not a horrible bug I mean after all I now get a free perk but just thought I let people know about it.

Interesting, I was planning on transforming my thief into a more assassin like character before doing the DB questline... kinda interested in seeing as you might "accidently" keep perks...

It's possible that it's not perk related. Pulling out a bow has always sped up my character considerably (especially while sneaking). The effect lasts for a few seconds before walking speed eventually returns to normal. For me it's always been like that, so it might be a very old bug that has always been there and that you just never really noticed before.

I thought that too, so I loaded an old save prior to putting points into Ranger drew the bow and saw how slow he was, he does move a little faster you're right but definitely not even close compared to having the Ranger perk.