I think we started using the term "ping" as well for calling someone to a thread.
I have no idea how ping got started here on FR, but I can only assume it was by someone who had been on the internet since the early days. Ping, is a program that you can run from the command line to find out if you can communicate with another computer. It sends a message to the other computer, and then returns the message back to you.
So ... if a Geek FReeper was on, and saw a message that they wanted to be able to review later, they could do that by "pinging" the thread, and therefore putting it in thier "My comments" section of thier membership (that is the return communication).
Bump, I imagine is similar, but probably comes from a Rush listener. Rush used to always refer to Bump music, which in his case is "Back to Ohio". When you hear that, you know the commercial is over and you are about to hear Rush again. So bumping a thread means putting it back in front of everyone's attention. Literally, with a new reply, it puts it back to the top of the "latest posts" thread. In short, it keeps the thread in a position of maximum visibility if a lot of people bump the thread.
If you "ping" (or bump, or put anything else in a comment) and send it to another Freepers name, it will show up in thier latest posts thread.
In recap, ping and bump both accomplish the same thing, they just come from Freepers with different backgrounds. Both are using the tools of Free Republic to either make it so that you or someone else can find the message again later easily, and so that other Freepers can see it as an active thread.