Unless you want to be phoneless and faceless you are being tracked wherever you go in modern large business.

Faraday phone cases exist, now.

Also, it's not too hard to have a tailor sew this, or similar anti-conductive fabric into the pocket(s) of your pants.

Or just put the bag in your pocket, if you want absolute security - you can have a Faraday bag made exactly to fit your phone, so it's no bulkier than a phone case like the one above (the bags, off-the-shelf, are LEO/mil-quality).