The Wikipedia article is as ever a good place to start but doesn't cover my specific question about why fly on to North Africa rather than return to England.
'Shuttle bombing' was the tactic of mounting a bombing mission from one set of bases and, instead of returning from the target to the original bases, continuing on to land at a different set of bases. The mission force would refuel, rearm and return to their home base in another mission on a later day.
The purpose of shuttle bombing was to confuse the enemy as to the bombing force's course, to wrong-foot him if possible, at least to keep him guessing. The hoped-for advantage would be to reduce bomber losses on the return leg of the mission, by misdirecting and dispersing enemy fighter interception.
It was soon seen in WWII that the greatest threat to day bombers was fighter interception, especially when the bombers flew without fighter escorts.
German ground control used effective radar early warning and tracking and excellent communications to command fighters from all over the Reich against USAAF deep penetration raids. Interceptors were gathered and held back until short-ranged escort fighters had left for home, then were flung in concentrated formations against the bombers, inflicting heavy losses.
The USAAF used a number of tactics to limit the interceptors' advantages during the run from home base to target. Spoof raids and diversionary raids were flown with small numbers of aircraft, in hope of delaying German recognition of the main mission force. The main force often flew an ambiguous, indirect course that could resolve into several different targets, and sometimes seperated and struck multiple targets, in order to delay German recognition of the main target. When they worked, these tactics forced the Germans to disperse their fighter resources to cover multiple potential targets.
But once the bombs dropped and the bombers turned for home, deception ended. German ground control was able to concentrate maximum force against the returning bombers, and losses were often heaviest on the return leg of the mission.
The tactic of shuttle bombing introduced deception and misdirection into the return leg of the bomber mission. If the Germans concentrated fighter resources on the route back to home base, they might be caught flat-footed when the bombers
never
turned
around
but continued on to their alternate bases. This happened with the Regensburg raiding force, which largely avoided further losses to German fighters, although bombers were lost to the length and rigors of the flight to North Africa.
Where a raid could possibly develop into a shuttle flight, a prudent German fighter controller had to position some of his forces to cover other lines of retreat, besides the one that returned straight from the bombers' target to their home bases, or risk the raiders making a clean getaway on their return flight.
The USAAF continued to use the tactic of shuttle bombing throughout the war in Europe. Later in the war, raids that shuttled between bases in the UK, Italy and the USSR achieved mixed success.
The greatest difficulty in shuttle bombing was developing the alternate bases. Massed groups of heavy bombers could not operate out of improvised grass airstrips. It took time and cost money to build suitable bases with concrete runways, hangers and other permanent building, inventories of spare parts and tools, stores of fuel, bombs and ammunition, and the ground forces to operate and defend them.
Even where the alternate bomber bases existed, as in late-war Italy, it took extra planning and effort to stage 'guest' bomb groups through them on shuttle missions. The attempt to operate from Soviet bases ultimately failed, because the Russians were unable to provide the base security that the USAAF required for normal operation of its heavy bombers – the Germans found out where the bases were and bombed the hell out of them, destroying hundreds of American bombers and escort fighters on the ground.
Flying the Regensburg raiding force from the UK all the way to North Africa was a mighty far fetch, and excessive operational losses occurred. Later in the war, the distances covered on shuttle bombing missions were not so great. The Regensburg plan may have reflected USAAF over-confidence, at this stage of the war, in their ability to execute ultra-long-range missions. The Tidal Wave low-level attack on Ploesti might be another example. That innovative and daring attack was completed as ordered, and scored heavy damage on the target – but at a cost of nearly 1/3 of the raiding force.