You'd need rather more than one bee, and you'd need to be stung on a pretty regular basis. Bee venom has been found to have anti inflammatory properties, and some pain relieving effect if used in acupuncture points, but this would appear to be symptomatic rather than protecting you against having arthritis. Plus any benefits would have to be weighed agaisnt the potentially severe effects of allergy to bee venom. (And it's not particularly kind to the bee, either.)
another fashion is arthritics squirting WD40 on their joints, i remember the radio2 phonein on its effectiveness, the results were inconclusive but the number of people phoning to say they too used WD40 was many, bee stings was mentioned too. a good thing against arthritis is to take codliver oil capsules.
I seem to remember reading a long time ago that Jack Warner (of Dixon of Dock Green fame) suffered from arthritis, and tried bee-stings to give some relief. Unfortunately I cannot remember if it did any good...