Depending on what actually needs replacing - a solenoid typically runs about $20 and is a terminal-connected item that takes about 3 minutes to change out, so minimum service charge of maybe $60-120 would be charged, plus the part.
The reversing valve itself (about $40-200 typically depending on model) is connected into the refrigerant line so the gas has to be extracted, the valve cut cut in the line (threaded or soldered depending on model), then the system pressure tested and repressurized which is a couple of hours work - so you are looking at a fair price of probably around $350-500, though I have heard of a number of cases where people were charged $1000 or more - probably by contractors trying to sell them a totally new unit.
I would question why the reversing valve is suspect - from what I hear from A/C techs, the defrost board or the solenoid are far more commonly the problem than the valve, so just the fact it is not reversing does not mean the valve is bad.