Today the number of submarines with some SAM capabilities is very very low, but this begins to change. It is very logical that in the future, strategic bombers that habitually work over the sea begin to have also some protection vs submarines. And the Tu-22 is not unknown in the Russian Naval Aviation.
There is no version of the Tu-22 or the very different Tu-22M aircraft that are strategic bombers.
Tu-22M naval aircraft are not fitted for any weapon that would allow it to engage a submarine directly.
there are some fuses that can be attached to conventional bombs so they can be used as mines in shallow waters but that is it... and unless the sub puts its periscope above the water for the Backfires radar to detect then it wont find them either.
This is not about today, obviously, and less about aircrafts out of service like the first generation of the Tu-22, but if you want, would not be bad if you do the list of models of submarine that have SAM capabilities today, and their owners. Today are very few. In the future is likely to see submarines and strategic bombers (also supersonic) being able to engage.
First the supersonic aircrafts were very vulnerable, later when we realized that they can have a strong and effective escort flying at supersonic speed, the operation was too expensive (like Desert Storm, no less), and now, when we realized that would be a transport operation of less than 24 hours (likely without fire), there is a problem with strategic bombers of today engaging future SAM submarines. Well, we are advancing, we need only to realize that future supersonic strategic bombers for sea work, likely will be able to engage future SAM submarines.
Still, not so sure if you keep in the mind the right definition of strategic bomber, and of which are the strategic bombers of the last decades and today:
wikipedia wrote:A strategic bomber is a medium to long range penetration bomber designed to drop large amounts of air-to-ground weaponry onto a distant target for the purposes of debilitating the enemy's capacity to wage war. Unlike tactical bombers, penetrators, fighter-bombers, and attack aircraft, which are used in air interdiction operations to attack enemy combatants and military equipment, strategic bombers are designed to fly into enemy territory to destroy strategic targets (e.g., infrastructure, logistics, military installations, factories, and cities). In addition to strategic bombing, strategic bombers can be used for tactical missions. The United States, Russia, and China maintain strategic bombers.
Weapons loads can include nuclear-armed missiles as well as aerial bombs
United Kingdom Avro Lincoln (22,000 lb)
United States Lockheed P-2 Neptune – small number converted as carrier-launched nuclear-armed bombers which would have to ditch/recover at land bases
United States Boeing B-50 Superfortress (28,000 lb)
Soviet Union Tupolev Tu-4 – reverse-engineered version of B-29 Superfortress
United States Convair B-36 Peacemaker (72,000 lb)
Soviet Union Tupolev Tu-95 (55,000 lb)
United States North American B-45 Tornado (22,000 lb)
United States Boeing B-47 Stratojet (25,000 lb)
Soviet Union Myasishchev M-4 (52,910 lb)
Soviet Union Tupolev Tu-16 (20,000 lb)
China Xian H-6 (20,000 lb)
United States Boeing B-52 Stratofortress (70,000 lb)
United Kingdom Vickers Valiant (21,000 lb)
United Kingdom Avro Vulcan (21,000 lb)
United States Douglas A-3 Skywarrior – nuclear-armed, carrier-based
United Kingdom Handley Page Victor (35,000 lb)
United States Convair B-58 Hustler (19,450 lb)
France Dassault Mirage IV (16,000 lb)
United States General Dynamics FB-111A – strategic bomber version of the F-111 swing wing strike aircraft
Soviet Union Tupolev Tu-22 Blinder (20,000 lb)
Soviet Union Tupolev Tu-22M Backfire (46,300 lb)
United States Rockwell B-1 Lancer (75,000 lb – use of external hardpoints restricted by START I)
Soviet Union Tupolev Tu-160 Blackjack (88,200 lb)
others designed and built which did not enter operational service:
Soviet Union Myasishchev M-50 Bounder
United States North American XB-70 Valkyrie
Soviet Union Sukhoi T-4 Sotka
Post Cold War
United States Northrop Grumman B-2 Spirit (40,000 lb)