Ping time is always round trip “latency” <——-> between your platform and a traceable site. Bandwidth per se, is NOT a variable that refers to “ping”. What really concern Bandwidth “capacity” would be the type of “loads” -applications- you are using a particular server site to implement. In other words; Bandwidth’s requirements will be different if you are implementing lots of graphics on the server side, or simple documents.
A ping packet is a 32byte packet of information so you will need at least 32 bytes of bandwidth to get the packet there and back.
Actually the ping (ICMP echo request) payload depends on the OS. There is also a 20 byte IP header and an 8 byte ICMP header + payload (32 bytes Windows, 56 bytes linux). In fact, the -l (lower case L) switch on the Windows ping will send whatever buffer size you want. This is a useful test to see how a link responds under load.
See this blog entry for additional information Network speed & capacity are NOT the same.