I'm moving house to Bathgate and the exchange their says it has fibre but our new house is exchange only line, so will I be able to get fibre?
No, not at present. You need to be connected to a cabinet to get Fibre to the Cabinet. BT/Openreach are going to place cabinets outside exchanges sometime in the future but it is not top of the priority list.
The Bathgate exchange has been FTTC upgraded and accepting orders
Try entering the properties address into here: http://dslchecker.bt.com/adsl/ADSLChecker.AddressOutput and copy and paste the results into a new post though remember to edit out the address.
Looking at other EO lines on the Bathgate exchange and near the exchange it looks like FTTC fibre broadband is not available to those properties due to the lines not being connected to a cabinet.
Therefore it looks like fibre broadband is not currently available to Exchange Only lines.
There have been cases where Openreach have installed a PCP and FTTC DSLAM cabinet outside the exchange building to accommodate those Exchange Only lines close to the exchange and to make FTTC available to them.
EDIT: sorry gg30340 didn't see your post.
So why can't BT just put the tecnology in the exchange building and just move over the wires like they would do from one cabinet to the other
Because they are not allowed to put cabinets into the exchange. They are planning to put cabinets outside exchanges sometime in the future but it is apparently not top of their priority list.