It is more than likely that you aren't being bugged. The network issue might well be just a misconfigured home router.
You have two possible choices:
- Technological (wireshark/MITM) to look at network traffic
- Sociological (trick your employer into admitting it)
Assuming that you aren't bothered about risking your job, then you could always do something that triggers your employer to act in a way that demonstrates that you are being monitored.
I don't have any great ideas of what you could do, but please make sure it is legal and ideally doesn't break your employment contract!