Strategic bombers don't have to carry strategic weapons.
A stealthy one however, has the ability to carry payloads equivalent to that of strategic weapons, but under the guise of stealth. However, a non-stealthy one obliviously does not have that guise. Thus, carrying around that heavy of a load, without stealth, and planning to use it against a hardened bunker, is not feasible until they get a stealth bomber (as a hardened bunker would more often than not, be protected by SAMs).
In a strategic nuclear conflict it makes much more sense to use a nuke rather than a heavy conventional weapon.
However Russian strategic bombers have previously been strictly nuclear armed cruise missile carriers, which means their primary role has been long range (ie strategic) and nuclear in nature.
What has changed is that they are adding precision guided conventional weapons to their arsenal, and also adding to their roles.
Instead of pure strategic nuclear cruise missile carrier, they now have the added roles of both theatre heavy conventional bomber and strategic conventional bomber/cruise missile carrier.
In a strategic conflict where nukes are not viable weapons... the best example I can give would be USAF B-52s flying from US bases to bomb somewhere a strategic distance away and then returning to the US.
If the enemy air defences are intact then they can use 3,500km range Kh-555 missiles with conventional warheads to begin to take down air defence sites and air bases while remaining out of range of enemy air power. They would likely operate with inflight refuelling aircraft and have fighter support... either Su-35s or PAK FA aircraft.
Once the enemy air defence has been reduced to a safe level then they can fly medium and high altitude missions to take out targets suitable for the FOABs, which would not include hardened bunkers as this is a fuel air explosive weapon that wouldn't be very effective against a hardened underground bunker.
An FAB-9000 would likely be more effective against an underground hardened bunker than this weapon, which is more like a daisy cutter.
If they wanted to play the US game of shock and awe and scare an enemy country with a really big firework display then this would be ideal... probably quite pretty over water...
Otherwise it is a very specialist weapon... though if a Chechen rebel camp is found in the mountains it is fairly unlikely they will have a huge underground complex so a single FOAB dropped from high altitude.... they wouldn't know what hit them and likely the entire camp would be removed from the map.