You can use Wireless range extenders (which may be what you mean by bridging) which need no Ethernet cable. They receive from your existing WiFi router, and retransmit.
The problem is that they cannot send and receive at the same time (or at least the affordable ones can't). The end result of this is that each range extender you use halves your maximum WiFi speed when you connect to it.
This may be OK for you, or it may not.
There are some really nifty little range extenders out there. I particularly like the BT branded ones, like the BT Dual Band WiFi Extender 600.
But it may be better to use a mains-based extender in one way or another. Essentially you use the mains cabling using special adapters to extend your wired network. You can plug a WiFi router into the remote end to extend your WiFi range without necessarily halving the speed (though don't expect massive speeds over the mains cabling in all cases).
Again BT have a wide range of products branded in their name that can help you. Take a look here: http://www.shop.bt.com/category/networking,network-d...
They have products that combine the mains extending and wifi all in one - plug one little gizmo next to your router, then you plug little WiFi extender gizmos wherever you have poor signal. BT WiFi Home Hotspot 500 does this, for example.
But BT isn't the only company that has this sort of kit, nor is the BT shop the only place you can get the BT-branded stuff. Check out Amazon where you'll see a million and one options.
Makes to search for are Devolo,, TP-link, D-Link and Netgear.
The Ethernet-over-mains technologies are known as Powerline and Homeplug
Amazon has most of the products in a "PowerLAN" category: Computers & Accessories : Networking Devices : PowerLAN Adapters.
Other things to search for would be "WiFi range extender".
Just keep in mind that mains-based products can work really badly. None of the properties I've wanted to use it in have been a success. Things like fridges, freezers, central heating and all sorts of other things can introduce a lot of noise that causes problems.