Is my iPhone bugged?
Yes, there are ways - though detection depends on what kind of bug we're talking about.

Is it possible to bug a non jail-broken iPhone: Yes.

Remember that a bug does not have to be in software - it could possibly also be in hardware. It also doesn't have to be in the actual phone, it could be placed in the cell network or in your providers systems.

In order to detect bugging, you could use equipment to scan for out of the ordinary radio emissions. You would also need to use a tool such as Wireshark to monitor network transmissions from the phone.

However a bug could elude such detection by being for example remotely activated or timed. Then you would need to employ your detection tools when the bug is actually active.

All in all it is very hard for an "ordinary Joe" to be certain that a phone is not bugged.

However, it is very unlikely that your phone is bugged if you really are an "ordinary Joe".