Chestnut. You are wrong. I travelled on a bus yesterday. I live in a busy city and commuted to, from and in London for most of my fifty years of working life. Now that I am retired, I still travel to London regularly and use my bus pass on travels all over the country.
I don't recognise the bus free for all that you seem to be describing "you do whatever it take to get on the bus". If I am third in the queue I will be the third person to get on the bus. If there are only two spaces, I won't be able to get on.
Wheelchair users have priority. This is what the bus company's accessibility charter says:
Of course, wheelchair users have priority over everyone else for the use of the designated wheelchair space, since this is the only place in which they can travel safely. Non-wheelchair users, unlike wheelchair users, will normally have a choice about which part of the bus to sit or stand in.
Common decency and respect for wheelchair users should mean that other passengers make way for them. Passengers are urged to offer cooperation in allowing proper use of the designated wheelchair area.
If the wheelchair space is occupied with a buggy, standing passengers or otherwise full, and there is space elsewhere in the vehicle, the driver will ask that it is made free for a wheelchair user. Where a pushchair or buggy is occupying the space, the driver will ask that it is repositioned, moved to another part of the bus or folded and stored in the luggage space, where available.
If passengers do not respond to such a request, without good reason, and the bus is not full, the driver will advise passengers that they are required to move from the wheelchair space. The driver will consider other action such as not setting off from the stop until the situation is resolved.
The same courtesy should apply to carers with buggies and I would hope that they show courtesy to one another. I don't think this woman did but I can see that I am in a minority so shall leave it at that.