Hot Spot Capture

I would like to pickup a wireless hotspot from one area and distribute
it though a router in another.

Here' my plan.
1) Setup a wireless ethernet bridge in an area where I can pickup the
hotspot signal.
2) Connect the ethernet bridge to the wan port of a router.
3) Connect to the router from my computer using a wireless connection.

wireless ethernet
wireless
hotspot <------------>ethernet bridge<-----------> router
<----------------->computer

Will this work or are there problems that I don't see

Sean