I think the question of whether the bursary holds good throughout your son's time at the school is one which you would need to ask them about. I don't know much about bursaries but I do think it is more difficult to get a bursary now and I suspect that you will have to regularly show them your eligibility for this.
The dilemma of choosing between grammar and indie is a difficult one. I doubt you would make a bad decision whatever you decided to do. You mention that you would not need to move house if you accept an indie place. This will presumably save you a considerable amount of money which could be offset with the expense of a private education. That is good news. However, there are many other expenses to consider with private schooling not just the basic fees. So, even with a reasonable reduction, parents are still expected to pay for many other things that the school offers. This could put you in a difficult position in the long term.
A couple of years ago, my son was given a place at a private school but he then got offered a place at our local grammar instead. It was an easy decision for us to go with the grammar school because it was the best school for him. It was also a relief not to have to pay school fees especially as I already have a daughter at an indie. The overall cost would have been huge for us so I am very grateful for how things worked out.
If you were to accept an indie place would you be looking at continuing into Sixth Form as well? This is another thing to think about.
It will not be an easy decision for you to make but, from experience, it is a big financial commitment and one which needs a lot of thought.
It is a good dilemma for you to be in though - a good indie and a good grammar! It could be much worse, the alternative being a local school which you don't like at all.
Good luck with whatever you decide to do.