I’ve used a Mountainsmith lumbar pack (like a big fanny pack) as a commuter bag, in lieu of a dedicated bike pack, or a two-strap backpack. I wore it a little higher than I would for hiking, at the waist, rather than on the hips, so when you’re leaning forward on the bike, it rides on your mid-back, rather than on your tail.
There are a number of cross-body bags in the EDC (Every Day Carry) space that might work as well. Smaller than a classic Messenger Bag, they wear at or below the shoulder blades, but you can still get them around to the front for easy access. Some of them are pretty low-key, or you can go ’Tacti-cool’ if that’s your thing