The rules on carrying bikes on trains vary with the different train companies. When there are insufficient places, it is up to the discretion of the guard as allowing any more on.
I would have thought that having a reservation for a bike should ensure that the place is kept clear but nothing surprises me about the ridiculous way our trains are run.
On my local line it is not possible to reserve a bike space. Cyclists are expected to wait at the platform until a train arrives with an empty space. As there are only two places per train this can be a bit of a gamble.
Good to see you have your priorities sorted though.