Bear's Oil was a hair preparation which was produced and sold by almost all reputable Perfumers, and many Druggists in the early 19th century. According to Putnam, the product was advertised as early as 1822. Originally, the preparation was made with actual bear oil, but, according to Cristiani, the problem with it was that it was hard to come by and became rancid very fast. I have seen several recipes for Bear's Oil, and they were all different. As a general rule, they were a mixture of other essential oils as selected by the individual Perfumer.
One could make a nice, small collection of Bear's Oil bottles. For some examples of Bear's Oil bottles embossed with Proprietor names, see Gallett, Glenn, and Swan. Description of #4, courtesy of John O'Dell. The drawing below illustrates a few examples of Bear's Oil bottles I've had in the past. Some known Proprietors of Bears Oil were: