In my Po Campo Six Corner Handlebar Bag you can see that it can fit in quite a bit.
Here I have my LV wallet, my Samsung phone, a set of keys and a tube of handcream by Crabtree and Evelyn. Sometimes I leave the wallet at home and take out the essentials and fit it into the zipped compartment inside the bag which means I can fit more things in.
It goes pretty much everywhere with me. On the bike, to the shops, at the beach to the park and it has a handy shoulder strap too that has thread that reflects light.
I have taken this bag on a boat where I ended up having a water fight and it kept everything inside it dry.
It really is a multipurpose bag.