At various times of day my beardies just sitting around and her mouth keeps falling so that her lips are just ever so parted[see the attached photo]. Does anyone know what this could be? Her temps are just fine, her appetites great like always and her last poop was 2-3 days ago.
It's not unusual for them to sit with their mouths open (even just a little like you're describing). I don't see the photo you uploaded. You can upload it to the site here https://www.beardeddragon.org/useruploads/ and then use the XIMG button to add it to your post.
Other than the lip thing she does, shes been hiding under her log and just acting pretty sluggish. Shes been hanging out on the cool side of her tank-- It isn't too hot in the basking area(Temp is only 103 to 105)-- and sitting in or near her water. Currently she is under her log just poking the end of her nose out. Her appetite is still great. The only two things that come to mind is that I added a reptisun light recently and that this is her third day without pooping.
It looks like shes trying to fall asleep. Shes just resting her head on the ground and pancaking under her log. Should I try giving her a bath or just leave her be?
That doesn't look concerning to me. Do you see any swelling along the gum tissue in the front of her mouth? She looks OK and no signs of distress like a dark beard. I'd probably let her be if she wants to hide on the cool side for a while.