What precise diplomatic humiliation could a Konrinental Bund inflict on Britain and how?
We have an example with the US, which used the war to change the agreement with Britain regarding the canal linking the Pacific and the Atlantic. Before that they were
It differs on goals and how well the partners of such a coalition could use it. For example, the 2nd Boer War would not end with an absolute victory for Britain but through pressure from the three it is changed into a mediated solution granting the Boer complete independence. A likely scenario would be a call for a conference and there Britain is completely isolated. Such a position would lead to a bad result for them and likely bring the British government down. In the end, this would take the Horn of Africa out of British hands down the line.
Then there is the Egyptian Question and here France could gain some concession. Any reduction in power in Egypt would be a slap in the face for Britain. France either getting an equal standing in some questions regarding Egypt or changing the convention of 1898 into their favor are both likely scenarios. With their stronger focus on Egypt, I would see them angling into that direction more than otherwise. The British de facto occupation had no legal leg to stand upon and enough pressure, as the French tried to bring upon till the Entente Cordiale, could easily make them back down if the situation looks bad enough. A continental alliance was the worst nightmare that British diplomats could think of, so it is unlikely for them to go for brinkmanship instead with an already escalated Boer War on their hands.
For Russia, at the time, it had a stronger focus on the Asian theater instead of the Balkan. Therefore, concession in that area are the most likely. From seemingly useless ones, like a harbor at the Gulf to concessions in Afghanistan, Persia and China. They can reach from drawing a favorable demarcation line to putting Russia into a position similar to after the Boxer Rebellion. Allowing them to fortify their position in Mandschuria and leading them towards a confrontation with Japan.
Russia had often been contained or hamstrung in their expansion or projects by their Southern neighbors, Imperial Germany and the Austro-Hungarian Empire. They could not start quarrels with them and also deal with Great Britain in Asia. Therefore, they always tried to keep the area where they are not focused upon quiet. With the Balkan Entente with A-H, they had postponed any disagreements between the two powers into the future. When Germany would instead of being an interfering factor be a supportive one, like in the Triple-Intervention in 1895 against Japan, they could get away with much. I would easily see them as the greatest immediate benefactor of such an alliance, but in the long-term they could easily suffer the most.
For Germany, most likely are arrondations of colonial territory, either through France as payment for diplomatic support or from Britain itself. Africa is the most likely region for that. Also in China there could be a new treaty reducing the monopoly position Britain held for most of it. I think Samoa re-emerged from being a non-entity into the focus at that point, which would maybe lead to a better settlement for Germany. For Germany, I would see less direct benefits, but far bigger long-term gains.