What are the costs involved in doing a border run and will my school pay?
Very difficult to answer this question. You could take a cheap minibus from Bangkok to Aranya Pratheet on the Cambodian border and still have change from thirty dollars. Or you could fly to Singapore and stay a night in a swanky Orchard Road hotel.
Border runs can be tailored to fit most budgets.
Schools almost rarely/never pay for a teacher to do a border hop or consulate run.