This is a tricky one, because it's hard to narrow down to just bombings - almost every major city to fall in the latter half of WW2 was bombed first, but how do we assess how important the bombing was to its capitulation? Would Dresden have resisted the Allied advance more if it hadn't been bombed? It's impossible to ever know. However, it is important to note that bombardment in the lead up to assault (from the 100 Years War to the Gulf War) serve to 'soften' an area by encouraging civilian populations to seek shelter and undermining military resistance and sapping resources away from the front line.

So let's look at two examples, one from 1807 and one from 1945, where cities or countries capitulated to demands where bombardment was the primary strategy used.

The 1807 Bombardment of Copenhagen is an early example (the people of Copenhagen like to refer to it as Europe's first terrorist attack), which achieved all its goals. They wanted to take the Danish naval fleet, to prevent it ever being used by the French, and to achieve this they bombarded Copenhagen with 'bomb vessels' (small but heavy mortar carrying ships) and rockets - after two days, and 195 civilians killed and 768 wounded, the city capitulated. They also besieged the city by land, but the bombardment was specifically to undermine the populace's morale and force the city to surrender without a lengthy siege or costly assault.

Over a thousand buildings were destroyed at Copenhagen, many set alight by rockets, and it quickly became clear that it was a choice between lose the fleet or lose the fleet and the city.

An extreme example would be the American nuclear attacks on Hiroshima and Nagasaki - which equally demonstrated that the USA had the power to completely destroy Japanese cities. From the American perspective it was the same reasoning that the British had used nearly 140 years earlier - demonstrate overwhelming destructive power and a willingness to use it to force a surrender early without having to engage in long expensive sieges and dangerous assaults.

So yes - bombardment can work to force a surrender. Failed bombardments (famously the German bombing of Britain during the Battle of Britain/'The Blitz') typically failed because they weren't destructive enough. If Germany had been dropping nuclear weapons or destroying the same ratio of buildings as Britain had in Copenhagen (500 a night in a city as small as 1807 Copenhagen is not sustainable) then perhaps Britain would have withdrawn from the war. But without overwhelming destructive power and demonstrable willingness to use it is unlikely for bombardments to be 100% successful on their own.