US visitors may get in on a driving licence, but the immigration officers are not keen on this form of documentation. Visitors from most other countries are usually granted a short stay on arrival, and tourist visas are not necessary. Officially, you must have a ticket back to your country of origin as well as an onward ticket to be allowed in.
Immigration officers do check.
You will also need an accommodation address on arrival, they do not check your reservation but if you say you do not know where you will be staying, you will be sent to the back of the queue and helped to select a hotel at least for one night. State the maximum period you intend to stay on arrival. Overstaying is not recommended if you wish to re-enter Barbados at a later date. When visiting the Immigration Office, which is open from 0830-1630, you will need to take your passport and return ticket. Tickets are inspected quite carefully.