You won't get a bursary based on potential future housing costs.
You will be expected to live much as you do at the time you are assessed, so moving to a more expensive property will be frowned on (unless its for a wholly unavoidable reason such as addition to the family and over-crowding otherwise)
So you need to start looking instead for cheaper areas within the footprint of the school's coach service, or which have easier public transport links.
KCS has pupils from a huge area. Living very locally is neither expected nor needed.
What other schools will you be applying for? And are you applying for any state schools as well - because those are the applications where address matters. And if affordability of private schooling is marginal, then you may conclude that state school is the better way forwards. So if you need/want to move, think also about state schools and being fully into your new home well before the cut off date for applications in your DS's round.
Generally, bursaries are offered to pupils who the school wants to join. KCS is, AFAIK, pretty straight - the bursary assessments are completely separate, and all boys are assessed in the same way. Only when the ranked list for offers is produced is financial need looked at. And they go down the list, offering bursaries until the bursary pot in empty. So if there are a lot more bursary candidates than funds available, then yes, you might miss out on being offered a bursary. But that's not because they are deliberately requiring a higher standard from those candidates. It's the reality that bursary pots can't always stretch to cover every applicant who meets the quality line.
Several schools are explicitly trying to achieve full "needs-blind" entry; maybe one day one or more will have a large enough pot to do so fully.
Other schools may assess bursaries in different ways (eg looking at what else the prospective pupil might bring to the school, whether that's in academics or co-curricular activity). But they'll still be balancing the pupils they want to bring in versus the size of the funds they have to make awards