Sciencealert.com has a story about why mosquitoes are more likely to bite some individuals than others. The conclusion is that the variable appears to be the microbiota resident on our skin, and the extremely subtle aromas to which they give rise.
My dear mother, for example was rarely bitten in outdoor locales where my father and I would be targets. My dad, who was devoted to her, liked to tease it was because she had "bad blood." She took no offense, probably pleased as anything to avoid the welts and itching we suffered in those pre-DEET days.
Consumer Reports says Avon's Skin So Soft Bath Oil doesn't work very well as a mosquito repellant, and Avon denies that's an intended usage. If you'd rather avoid DEET, CR suggests trying repellants with Picaridin in the 20-30% concentrations.