You might be having a reaction to one of the ingredients.
Dr. Bronner's Castille soap contains Tocopherol, a class of chemical compounds related to Vitamin E. It is probably included as a preservative, as Tocopherols prevent oils from becoming rancid. (The peppermint soap contains, according to the label, coconut, olive, hemp, jojoba and peppermint oils.)
Some individuals have allergic reactions or develop rashes and hives when Vitamin E is used topically (on the skin). See:
http://www.dermweb.com/skintherapy/stl0103.html#RTFToC6
Excerpts:
"Onset of symptoms was 1-160 days (median 14 days) after first use of the cosmetics. The lesions were long lasting, widely distributed, associated with a pronounced pruritus, and frequently aggravated by sweating, solar irradiation, or heat. The rash subsided within 1-4 weeks following topical or oral corticosteroid treatment but sometimes relapsed after sun exposure."
[Interesting about the sweating and heat, which are typical during a bike tour...]
"Mennen's "E" deodorant aerosol caused so many cases of allergic contact dermatitis that it was withdrawn from the market."
"Thus, as well as limited utility, topical vitamin E can produce a completely opposite reaction to that intended, damaging the skin rather than "improving" it. Therefore, so-called natural vitamins are no different from many other cosmetic ingredients: they all have the potential for allergic reactions, some of which could be atypical."