Roll the bill into the fabric. Forms a crescent moon shape. Shove it under your belt

Or just be bald. I never have helmet hair.

That pip on the top of a baseball cap is dangerous under a helmet. Its essentially saying, ‘hey coordinate all the shock right here’ like a little pin hammer. Get yourself a cycling cap for under the helmet. Way more comphy too.

But yeah id go with the hook it to your belt loop. Maybe with a carabiner so you dont stress the snapback

Nobody cares where your hat is placed. Nobody is going to see it on your handlebars and think ‘what a twat. I’m going to tell everyone how big a twat this guy right here is. Unbelievable! The audacity.’

You’ll be just fine.

Get one of those kid’s seats for the bike, get a large stuffed… Tiger? Yeah, Tiger. Put the hat on the Tiger, strap the Tiger into the kid’s seat. Nobody will mock the Tiger for not wearing a helmet.

Would it look stupid to place the cap on the handlebars

No.

or clip the cap into the strap of the helmet to carry it while riding?

Yeah kinda, I’m imagining it hanging from your face?

If you have a snap back kind of hat, yeah just attach it anywhere on the bike I’d say, or depending what you’re wearing, to you in some way. Don’t over think it.

Here is a ballcap like hat I wear, that’s good under helmets, and it folds up and comes with a bag to carry it in.

Who cares about looking stupid. Just done what you gotta do.

Here’s what you do: get a bike rack and bungee core a milk crate to it. Bonus points for a milk crate that looks well worn and like it lived an entire lifetime before it took up residence on your bike. The look is timeless, a classic of style, unquestionable. From there you can store anything you want, hat included.

Or don’t. You wouldn’t ask a stranger on the street for their opinion, so why care what they think?

If I saw someone wearing a helmet, with cap strapped on somewhere, I’d understand. It’s practical, and it’s pretty clear that your planning to wear it when you remove the helmet, you’re not trying to make some sort of statement. Go for it! (as long as your cap strap is reliable…)

You’re overthinking it lol

If you’re wearing jeans you can also strap it onto the belt straps. If it’s on the side it shouldn’t be too uncomfortable

Practical is sexy.

I snap my hat to my bag or frame then swap helmet for hat when I arrive at my destination.

Spend less time worrying about a hat and get a proper helmet with a chin bar.