Just to be clear on what the judgement actually says (which is complicated by the fact that a number of the judges partially dissented)...
The policy of FirstGroup was that drivers should request that the non-wheelchair user vacate the space and do nothing further if met with a refusal. The Supreme Court has decided that this was inadequate. They believe FirstGroup should encourage drivers to go as far as they think appropriate in the circumstances to get the passenger to reconsider their refusal. What was appropriate might depend on why the non-wheelchair user refused to move, including the non-wheelchair user's needs, whether the bus is full, whether it is on time, the length of the wait until the next bus and (possibly) the character of the driver. If the driver thinks the non-wheelchair user's refusal to move is reasonable they would not, according to the judgement, be required to take any further action. If it is unreasonable the driver might be expected to rephrase the request as a requirement and possibly, in the face of continued refusal, refuse to move the bus for a few minutes to try and pressurise the individual into moving.
Some of the judges also suggested that the signs for wheelchair spaces needed to change but I haven't read the judgement carefully enough to see if that was agreed by a majority.
Note that the Court has not required bus drivers to behave differently. They have simply required FirstGroup to change from a policy of request and do nothing further in the face of a refusal, to a policy of requesting and, if faced with an unreasonable refusal, consider whether to take further action to try and persuade the non-wheelchair user to move.
Whilst this is being hailed as a victory for disabled rights, I tend to agree with those judges in the Supreme Court who have said that, in practice, there is very little difference between FirstGroup's existing policy and the new policy the Supreme Court requires.
Following this judgement FirstGroup needs to reword its policy and provide some training for its drivers. However, if they do so and Mr Paulley subsequently finds himself in the same situation, there is no guarantee that the outcome will be any different. FirstGroup will have discharged their responsibilities by setting an appropriate policy and providing training to drivers, so a similar legal action by Mr Paulley would fail.