Bump in its current iteration doesn't support using it with PCs. NFC could work in this context if the PC had NFC hardware on it. Upcoming laptops are supposed to have this, but I agree that it would be a rarity making it difficult to rely on. However there are various methods to sync with a PC. Have the PC display a QR code and use the smartphones camera to scan and connect. I believe Clik employs this, among other apps.
My point in pushing NFC over Bump is that it achieves all of what Bump is trying to without relying on an external service or data connection. It's beauty is its simplicity and relatively low friction to use it for impromptu data connections, especially with strangers and people you just met.