Hi Nancy,
There are a few different ways you can do this.
My husband and I recently purchased a car, and in anticipation we brought $10,000 cash with us from the United States (this is the limit you can bring when flying in). We then supplemented the remaining cash we needed just by ATM withdrawals.
Typically, as you probably know, ATM cards will have a $500 daily limit for cash withdrawal, however if you call your bank, in most cases they will allow you to temporarily increase the daily limit – in our case we bank with Chase and they allow you to increase to $1,000 per card. So we each called, and made those one-time withdrawals.
Another option, as long as you will pass through a city in Costa Rica with a location would be to transfer the money to yourself via Western Union, but there are fees associated with this so just be sure to look those up.
Hope this is helpful to you!
Jackie