Get larger bandannas or women's kerchiefs and scarves. Nobody will care. Just pick a pattern that suits you. Cheaper than caps and purpose-made cycling doodads. I have a couple dozen so I always have a fresh one. The longer tails allow knotting them lower near the neck, clear of the helmet.
If it's good enough for famous mountain specialist Sir Ben Kingsley, it's good enough for you.
Mountain specialist Sir Ben Kingsley, aka "Il Pirata".
The trick is to tie the ends closer to the neck, below where the helmet sits. This varies with helmet design. Some mountain bike helmets project lower on the back of the skull. Some commuter or skateboarder/skater helmets have more space at the back. Most road helmets are somewhere between the two.
Since I have long hair I have to switch from the man-bun to a regular ponytail before putting on my helmet. I was wearing the Rey samurai style double and triple bun long before she was a twinkle in George Lucas' imagination. But it doesn't go with bike helmets.