Swinging both ways can open up a lot of options, though if Katy Perry kissed a girl and liked it, why couldn't she just keep kissing girls, possibly in public? She's got a rack! For a bag brand that'll go two ways, grab Body-Kit.
Kit's a UK born-and-bred line of clean, versatile carry-sacks designed to be amenable to two wearing styles, "dynamic" (more body gripping, easier to rock) and "relaxed" (a little smarter & jauntier), the idea of a design team who cut their teeth making schlepping gear for the British Army, so you know their stuff is major.
Coming in blue, orange, black, or red, the bags are constructed from weather-proof nylon and laser-cut steel fixtures, and all have fabric-concealed expansion zips to double their capacity, with the exception of the Body-Grip, which can either be shoulder-slung (its relaxed mode), or unzipped into two torso-hugging halves and worn like a bulletproof vest, so you can finally feel safe from gunshots without carrying a bible/flask in your pocket.
There's also a two-some of hip-huggers, worn "dynamic" by securely belting round the waist, or "relaxed" up around the shoulder, one small and compact (the Body-Loop), the other laptop-sized and called the Body-Bank, also the place to go if something really does cost an arm and a leg.
The collection's rounded out by two messengers: the rectangular Body-Spin (which can be worn portrait or landscape either hanging near your waist or tighter up to your back), and the triple-pocket, high-capacity Body-Bag -- how so many people wish the paramedics would Get Him from The Greek.