Most charge £40 and above for a private transfer one-way. Gordion also charge £40, they and others may do it for less. At one time I used to get private transfers at £30, but not so easy now as fuel costs are high.
Earlier this year (not peak summer holiday season) I booked a shuttle transfer with Gordion and there was only 1 passenger (great!) so it was just like a private transfer but only cost the same as shuttle.
Just ask, name your price and see what they say? It's approaching end of season so you've nothing to lose.
I've just used Altinkum transfers, coach quite full, couldn't find driver with a placard when we arrived, so had to go round asking and eventually found them.
Its a long journey, stops 10mins on the way for a break -which may be ok daytime but at night you just want to get on with it. Then half way thru' the journey they asked us and another 2 passengers to transfer to an awaiting car and the coach drove off with the rest of the passengers to Altinkum.
In the hurry of changing vehicles half way thru my son lost a toy, see here