Clue: Ultimately stuck to bath oil that's in make-up bag (4)
Answer: KOHL
Explanation: Definition: that's in make-up bag
The flip side of the 'primarily' clue: last letters ('ultimately') of 'stuc**K** t**O** bat**H** oi**L**'. I do not think it would be found in every make-up bag, although mascara serves a similar purpose.