A "bug" can be a slang term meaning an urge, or a a desire. If I get bitten by the travel bug, that means I would like to go on a holiday, the sooner the better. In this case the "beauty bug" means the desire to look glamourous. Usually it's a human female that gets the urge to go to a salon and get a makeover, but in this case, it's camel owners using extraordinary means to make their animals "pretty."
The "trophy camels" are the camels that have won a prize in this competition. The phrase can have a double meaning in this sentence however, since the owners are dressing their animals up.... Often when an average-looking man marries a much younger, very glamourous woman, we call her a "trophy wife." Since these camels are groomed and pampered and manicured, they are the dromedary version of a trophy wife.
"Oodles" means a lot, a large amount. A millionaire has oodles of money, for example. In this case, oodles of camel accessories means a large variety of supplies to groom and dress their animals up with. The parlors have jeweled collars and other accessories for camels, as well as products to make their fur more colorful and attractive, polish for their hooves, etc.
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