Rectal gonorrhea is common in women and in men who have sex with men. Among women with gonorrhea, about 30-40% have rectal infection; in about 5% it is the only infected site. It is acquired primarily by anal sex, but also by contamination of the anal area with vaginal fluids. In these women, the exact mechanism is unknown, but it probably involves vaginal fluids coming into contact with the anus. But probably not because of direction of wiping, which falls into the folklore category. Despite claims online and elsewhere that it's a health issue, it probably makes no significant difference in genital or rectal infections. It is a common belief that urinary tract infections or vaginal yeast infections might result from back-to-front wiping, but research shows this has little if any effect. The same probably is true for rectal gonorrhea, and I doubt wiping direction makes any difference in risk of rectal gonorrhea or chlamydia.

Gonorrhea and other STDs are not just infections that happen to involve the genital area. The bacteria and viruses that caused them evolved to require sex itself for transmission. Frottage, hand-genital contact, fingering, and contact with an infected environment (toilet seats, towels, etc) just don't transfer enough bacteria for gonorrhea or other STDs to take hold. Even with vaginal sex -- with infected semen deposited directly in the vagina -- only about half of exposures to men with gonorrhea result in infection of the female partner.

Gonorrhea and chlamdia do not survive drying. But duration of survival outside the body doesn't matter. However long they survive, no infections result from exposure to contaminated towels, toilet seats, or in shared intimate clothing (e.g., panties, bathing suits). If you don't have sex with infected partners, you'll never catch gonorrhea. It's that simple.

I hope this helps. Let me know if anything isn't clear.