Stealth doesn't so much perserve the surprise element. The enemy generally knows the attack is coming and is in readiness. With total air supremacy that have limited ability to shoot down a Stealth. They'd need the golden BB. When their SAM sites come up for acquition of their blasted by a HARM missile off an F16. Stealth denies a radar acquition and lock on. And all the computer generated solutions to enable a shoot down. A visual lock on is hampered by night operations.
As for traffic separation. I'm sure there's several corridors that are used for the exclusive use of military operations. Crossing the North Atlantic is not done on the NAT. Land fall is probably somewhere over Iberia and an AWACC controlled corridor provided to the crews for ingress and egress.
Bombers generally have a TOT (time over target) they're controlling for in country. These times are deconflicted with other operations. You check in with AWACCS and they provide traffic reports and interrogations of possiblefriendly & hostile actions. In short, there's a plan. We own the air space. We divy it up for operations. And don't forget the time honored "Big Sky Theory" it still works.