Matt I think that Tesco is opening a little "Metro" in Claughton but I'm pretty sure that the big one isn't moving as they're spending cash on it at the moment with a new Petrol station and photo lab. Whilst we're talking about new supermarkets we shouldn't forget Morrisons being built in New Brighton.
The petrol station was shut down by health and saftey matey, they we're actually trying to avoid spending money on it, but the tanks needed re-lining and they we're forced to close it.
I have heard a few report's around the net etc that the Bidston one is considered "too small" by Tesco to serve the needs of local people and they have very limited expansion options now. I fail to understand where a new one would go in Claughton, but this is what I have heard on a few occasions. There is also reference to this on Wikipedia.
The other future problem they have at Bidston is the development of Wirral Water's, which will be just around the corner from it, and have an even bigger and possibly more customer-friendly ASDA supermarket.
I believe the proof of whether they are staying in Bidston Moss or not, will be whether or not they decide to go ahead with their proposed multi-storey car park there.
Personally, I would hate it to be closed, because it is the perfect location for me.