Will my bounty follow me to Cyrodiil?

Gedalya

If I have a bounty will it follow me to Cyrodiil? In other words, when I arrive at my Alliances starter zone(s) will there be guards I need to hide from?

UrQuan

Your bounty won't automatically go away, but because it's a war zone it won't be enforced either.

So short answer: no, you won't need to hide from guards.