I've been using a mixture of baby oil aka mineral oil mixed with Eucalyptus oil, Tea Tree oil and citronella. It's a home made fly repellent we use on our horses. Spraying this and brushing has removed the sticky bits from the bandaging. Most oils in fact will assist in removing the adhesive from the coat.
Some people prefer to use Eucalyptus oil or Tea Tree oil neat, but I am concerned about the harshness of an undiluted oil on the skin.
There's also products made specially for removing sticky plastic residue.
The other option would be a soapy warm water, but I prefer the oil option, as I didn't want to wet the coat unnecessarily, as she still has a bandage on her leg and I didn't want water running onto it.
I wouldn't recommend using an oil if the area needs to be re-bandaged with an adhesive bandage, as it will make it less likely to adhere to the coat. In fact, I've allowed the adhesive residue to remain on the coat so that it assists, if anything with the re-bandaging.