I've looked through the scripts for both The Matrix Reloaded and The Matrix Revolutions, and there's no explicit reason given to the audience because Bane/Smith can't remember what happened (at least, that's what he claims) and he's the only survivor.
We can rule out the hypothesis that Bane had control over the sentinels like Neo did. The Oracle explains that Neo's power over the sentinels is due to his special connection with the Source since he is the One:
Neo: Tell me how I separated my mind from my body without jacking in. Tell me how I stopped four sentinels by thinking it. Tell me just what the hell is happening to me.
The Oracle: The power of the One extends beyond this world. It reaches from here all the way back to where it came from...The Source.1
It is true that as an Agent, Smith did have the authority to command sentinels from within the Matrix (he orders a sentinel strike in The Matrix). But Smith is no longer an Agent so he no longer has this authority -- he has disobeyed the rules and avoided deletion, so he is an Exile. He is now an enemy of the machines and the Agents -- so the sentinels would be ordered not to obey his orders.
The only reason the sentinels might intentionally spare Bane/Smith is that they would potentially have an "inside man" during the attack on Zion. But the machines don't really need an "inside man" because they are confident in their victory -- they've destroyed Zion several times before and are getting "exceedingly efficient at it". Moreover, sparing Bane/Smith as the only survivor would make the humans so suspicious of him (as they in fact were) that he'd be ineffective as an "inside man" anyway.
Bane was probably knocked out by his own EMP blast (possibly because the Smith virus was in his head jack). That's why he was unconscious for awhile after the sentinel attack, and he wasn't faking that. My educated guess is that the sentinels thought he was dead or didn't notice his body when they started killing everyone in the hoverships. Whereas all the other humans would be actively fighting the sentinels, Bane/Smith was lying motionless and unconscious -- he would be easy for them to miss or to think he was dead. Even if the sentinels are able to pick up neural activity and discovered that he was merely unconscious (we don't know if they can sense such activity), they would have picked up unusual neural activity:
Roland: Has this man been tested for VDT's?2
Maggie: Yes, sir. It was negative. But, he is showing a lot of unusual neural activity. Some cross-synaptic firing as well as signs of recent trauma. With fresh fibrotic scarring throughout the cortex.
Again, with this unusual neural activity they probably thought he was dead3 (if they even noticed his body at all). It's quite possible the sentinels didn't even notice his body because they were in a hurry. Zion knew the machine army was coming, but the quicker they could attack Zion the less prepared the humans would be. The sentinels quickly attacked the disabled hoverships and moved on, as indicated in your quote:
Roland: Once the machines were done with us, they started digging again.
1 The Matrix Revolutions
2 I don't think it's ever been explained what VDTs are.
3 Brain activity after death seems possible. See, for example, here and here.