It varies so much from council to council and depending on the kind of property you need that only someone in the same council area and with the same needs could give you an idea, @JessicaHonhold.
Are you in private rented accommodation at the moment or is this just a transfer within the council? Transfers tend to happen quicker, because they can then relet your old house, so they get 2 households off the list.
I'm guessing you need a bungalow or g/f flat if you can't do stairs. Where I live, you could get somewhere quite quickly, eg 6-9 months, especially if you were ok with being in a small village. The council has a fair few one and 2-bed bungalows and because they tend to be let to older people they become vacant reasonably often.
"Bidding" is when the council publish details of vacant properties for people on the waiting list to express an interest in, ie "bid". The council will look at all the interested parties and the property will be offered to whoever has the highest priority band.
If you're eligible to bid, they will have given you a bidding number. Some councils prefer to let properties suitable for people with disabilities directly, rather than through the bidding system.
Ask your housing officer if you're not sure if you should be doing anything.