Not medical advice, but my experience -
I can't speak to outside the bathtub, but I brought baby to breast ASAP (nipple stimulation was the alternative). We expected placenta to detach easily. Angelica would have helped if it hadn't. Placenta was half-delivered and felt like it got "stuck" so I passed baby to my husband and got into a squat. Placenta delivered mid-squat and I placed it in a colander and basin until we were ready to cut the cord. I inspected it in the basin to make sure that there weren't any obvious broken pieces (like, "oh, hey, there's a large chunk missing from the placenta... we should check and make sure that nothing is retained!"). I massaged my belly every so often with arnica gel and used Afterease tincture by Wish Garden, which was recommended by a woman in my DDC.
I prepared for my birth by taking alfalfa tablets (Vitamin K for clotting) toward the end of my pregnancy as well as for quite a while afterward. (Baby is five weeks old.) I had shepherd's purse tincture on hand and drank white oak bark tea and RRL tea while in labor and while in the bathtub after birth. Your mileage may vary, but I remained in the bathtub for several hours after birth (taking care to keep baby warm/comfortable) and refreshed the water as needed. I had a FAR easier recovery with this baby than I had with my first, despite tearing significantly this time (I didn't realize it until several days later). I honestly believe that it was the time spent in the water after birth that aided in the healing - but again, just my opinion/experience. I have also heard (I think an Ina May or Gloria Lemay tip) that placing the lips around the lip of a narrow bottle, like a glass soda bottle, and blowing into the bottle will help dislodge the placenta - although I haven't tried it myself.
Hope this helps.
wife of my sun and stars
momma to tiny.human v1.0
tiny.human v2.0 summer 2014