I'd expect it to be some £hundreds.
An upstairs windowless bathroom probably has a duct going through the ceiling and running across the loft to exit at the eaves or a wall; or possibly going through a roof vent or tile.
Holes in the roof need to be done by a roofer, or rain may get in.
Your old duct may be adequate, and will probably be 100mm (4-inch)
if you were fitting a new duct, I'd go for rigid duct, sloping slightly downward towards the exit so that any condensation can run out. Flexible duct is very prone to accumulating water and fluff in the convoluted hose. If you need to fit a new duct, get a 125mm or 150mm, then you can have a bigger fan. a bigger fan can shift more air at lower speed. At extra cost you can have a different fan and a fan speed control. Then you can get a good powerful one, and turn it down a bit if it sucks harder than you need.
If the roof is very dirty, people won't like working up there. If you have old yellow fibreglass, I'd consider a dust mask and skin protection absolutely essential. Some people are hardier or less sensible
At a complete guess it might take a day to do a nice job with new duct, or an hour to just swap the fan.
a 100mm fan like this is around a hundred pounds. This one is a good make with run-on timer. It has about three times the power of the cheap fans usually fitted by builders and is quieter. as you already have a mould problem I think it would be suitable. It is single-speed. If you want a more powerful one I would go for speed control, and 125mm, it will cost more.
A loft fan should be fitted on a board, with an isolating layer of resilient foam or carpet underlay between the board and the roof timbers to cut noise and vibration.
I think the low noise is very important with a fan that may run frequently, including at night.
The wiring might need to be changed, so I'd choose an electrician for the job. Qualified people are listed on the Self Certification schemes such as NICEIC. Go for an Approved Contractor, not a Domestic Installer (which is the lowest grade). With a small local business you are more likely to get the qualified business owner rather than a junior. Mention that it is a loft fan. Have a look in the loft yourself so you know what it's like.