Cheapest border bounce from Bangkok at the current time is via Cambodia. There are companies that do trips to the border daily by van, which is convenient, slightly uncomfortable, and a bit more expensive than doing the trip yourself on public transport.
One option, if doing it yourself by public transport is Ban Pakard (Phsa Prum on the Cambodian side).
Take the first bus in the morning to Chanthaburi (about four hours and 200 baht or so), then local van or songtaew to the border . The van costs about 80 baht, as I recall; the songtaew is a bit cheaper. Either way, there may be a fairly long wait, and the trip takes a bit under an hour. You must leave Bangkok early in the morning as public transport back from Ban Pakard becomes iffy late in the day.
Crossing the border, you must buy a Cambodian visa on arrival. Have US$ available to pay as otherwise you will be charged a lot more to pay in baht. You are likely to be asked for more anyway. My policy is to try to resist the request for extra money, being sure to do this in a polite and friendly way, but some find it less hassle just to pay up. The official visa price is US$30.
By law, you are supposed to stay one night in Cambodia but, in practice, you can go straight back to Thailand. However, Cambodia immigration will likely want a monetary inducement to let you go. If asked, see if they will accept 200 baht, and (in a polite and friendly manner) resist a request for any more than 300 baht.
Arriving back on the Thai side, ask around to see if there is a van going to Pattaya. If not, retrace your steps back to Bangkok via Chanthaburi.
There will probably be agents on the Thai side wanting to handle everything for you, including the visa and same day return, for a premium (often almost double). This is less hassle. It is up to you.
The cost (best case) would be
about 400 baht Bangkok <-> Chathaburi
about 150 baht Chanthaburi <-> Ban Pakard
US$30 for the Cambodian visa on arrival
about 200 baht for same day return (possibly avoidable)
You might be faced with some unavoidable extra costs if things do not go smoothly.
It is a long, tiring day to do it this way, and would not be everyone's choice.