If you wear cycling shorts (which I would, for comfort) you can stash it in the shorts, in the front or back.
I’m sure you’re wearing a helmet, I also think cycling gloves are a good thing. I used to cycle to work a lot.
You can also stick it in your bra, or buy special underwear or shirts with pump pockets. Spibelts are good too. I’m just saying, I think you’ll keep it better protected if you keep it close to your body.