It's normal for a cruiser to operate alone without destroyer escort in some circumstances. A heavy cruiser is an important asset, but it's not a capital ship that will shift the balance of naval power if lost. Destroyers were always in high demand for various roles in world war two and there were usually not enough to go around. A cruiser task force going in to action might normally include some destroyers, but not each individual cruiser on a non-combat mission.

Anti-submarine weaponry in World War Two was generally only effective after the submarine was detected. An escorting destroyer would not have been able to detect the submarine and prevent the Indianapolis's loss, (high speed reduces the ability of surface ships to detect submarines) although it may have meant a ship was present to rescue survivors or counterattack the submarine. A heavy cruiser is much faster than a submarine (surfaced or submerged) and a fast speed and zig-zag pattern course (which the Indianapolis should have been following but wasn't) will generally provide as much protection as possible against the submarine's first salvo of torpedoes.

The main reason to avoid including destroyers as escorts to a heavy cruiser is range. Destroyers have a much shorter operating range than cruisers, especially at high speeds, and the voyage from Honolulu to the Marianas would be too close for safety to the maximum operating range of a WWII destroyer. Destroyers accompanying major task forces have to periodically refuel from supply ships or larger warships, which is time consuming and creates a moment of vulnerability.

Also, just to note: the path from San Francisco to Tinian was not especially dangerous at that point in the war. The Japanese Navy was no longer doing a whole lot in that wide expanse of the Pacific.

The atomic bomb components were only on board at that point (and it was not the complete bomb, either, nor was it all of the bombs, plural). The path from Tinian to Guam was more dangerous by a significant fraction, even if by that point in the war the Japanese Navy was no longer the force it had been earlier in the war.