Up until the 1930's lighter than air aircraft were the preferred method of long range air travel. This was due to the relatively low power to weight ratio's of contemporary aircraft engines, and their poor fuel economy. A lighter than air airship (blimp, Zeppelin or other LTA craft) displaces the air and is therefore not dependent on the power of the engine for lift. A relatively low powered engine (or engines) will do for most flight regimes.
However, since engine technology isn't advancing very rapidly in this timeline, the various world military forces have concluded that long range bombing missions will have to be done by airships. Of course, a long range airship bomber will need to go very fast in order to reach targets in an acceptable timeframe and to evade enemy fighters. Looking at the situation, the problem seems insurmountable, or is it?
Reaching targets quickly and evading enemy fighters will require the airship bomber to move far faster than any existing aircraft, and also fast enough to evade detection by air observers and anti aircraft cannon on the ground as well. Some advanced thinkers believe the airships need to travel at over 1236 KPH, the speed of sound in the atmosphere! While no engine or combination of engines and airscrews seems capable of performing these feats, advanced thinkers in a few nations think otherwise:
In the United States, the US Navy is aware of Robert Hutchings Goddard and his experiments with liquid fuelled rockets. The new Chancellor of Germany has been briefed on the activities of the VfR (Verein für Raumschiffahrt), and in the Soviet Union, rocket research is being carried out by GRID (Group for the Study of Reactive Motion). Rocket research isn't as advanced in the British Empire, but there is this Frank Whittle chap working on what he calls a "jet" engine.
While flying the entire profile at supersonic speed is perhaps a bit ambitious, how can our various military forces achieve at least supersonic dash speed over the target with a lighter than air long range bomber? Assume generally 1930 era technology for the airship, propulsion systems and bombs and bombsights, but some handwaves are acceptable.