If you do go ahead don't just buy a scooter from the internet, go to a place that will let you try different scooters.
There are two main types, class 2 and class 3.
Class 2 are designed to be used on pavements and can be ridden on to buses / trams / trains for some of the smaller ones. Their top speed is 4mph.
Class 3 are bigger, can be used on roads and have a max speed of 8mph. These do not fit on buses.
Do you need a scooter that folds down? Do you need one you can dismantle easily?
You cannot just get a scooter and go on the bus though, you have to take a sort of driving test to show you can manoeuvre forwards and backwards and you get a card from the bus company.
Where you take the bus test doesn't really matter as other companies accept the card / pass.
Where I am the trams have a different card but they will issue it on the basis of the bus test.
Finally but really important is insurance. Not so much for the scooter but in case your relative causes damage to a person or property.
Link to a documentary about scooters.