Such work must be done via a sparks, it's dangerous to attempt DIY where water and electrics mix.
The cable run would be via wall chase, inside hollow stud walls, plastic trunking or surface clipped.
A 16mm TE cable would be required and guess at a days work plus materials (fuse on board, pull switch in bathroom) will be about £400.
The there's the electric shower unit at about £150 with fitting and any adjustments to plumbing works, say £100.
So 'saving' you money will cost at least £650 and that's provided the electrical system is up to date since an RCD will be required and the earth bonding in the property must be up to date.
Did you know that heating water via boiler and gas is cheaper than via an electrical heating element (as inside a electric shower) ?
If you want to save money:-
Allow them a shower once a month
Make them share the shower
Tell them to use the school shower after sports
Send them on stay overs