But those bombs also prompted a re-think in Washington, convincing the United States - it is said - to revert to a more hands-on role (after several months of leaving well alone) and press for an accelerated fulfilment of the Oslo accords. This would bring the delicate matter of jurisdiction over Jerusalem onto the agenda sooner than either the Israelis or the Palestinians had envisaged.
If that is so, then Mr Ross, who has been shuttling around the Middle East for the last five of his 48 years, is seen by most observers as the only man for the job. His immediate task is to test the water to gauge whether further progress is possible - on that will depend whether the US Secretary of State, Madeleine Albright, makes her first official visit to the region later this summer.
Mr Ross, described by friends and sceptics alike (enemies would be too strong a word) as an apparatchik, takes a studiedly low profile, as he has done since the start of his career. He gives the impression of a grey, rather self-effacing man, more at home in the corridors of academe and the state department than in the glare of television lights. His middle initial, B, reportedly stands for nothing, it just fills out his name.
A Californian, who initially specialised in Soviet studies and Soviet policy towards the Middle East, he has worked in government - the Pentagon, the state department - since the late Seventies, with one break in the early Eighties when he ran a Soviet studies course at the universities of Berkeley and Stanford.
Although a Democrat, his front-line diplomatic role began when he became adviser to then Secretary of State, James Baker, as the Soviet Union was breaking up. His speciality was the impact of Communism's fall on regional issues, and his vast accumulated experience of the Middle East makes him, in the words of one associate, "indispensable", to the peace process. After a decade, he now knows all the players personally.
The strongest opinion ventured by sceptics is that Mr Ross has perhaps been shuttling around the Middle East for too long, that knowing the players could be a disadvantage and that, just maybe, Washington needs a fresh mind and a fresh face to tackle fresh problems, even though they are just aggravated forms of a very old problem.
One argument that is not advanced against Mr Ross in this context is his Jewish background. He knows Israel intimately and spends holidays there. His children are named Gabriel, Rachel and Ilana. Yet, it is said, his biggest recent problems have been not with Yasser Arafat or the Palestinians, who are said to have come to trust him, but with the Israeli Prime Minister, Benjamin Netanyahu.
Mr Ross is said to have had two liabilities in his dealings with the present Israeli government. Despite serving the Republican administration of George Bush, he is a Democrat - and since the reagan administration Democrats are now deemed to be less friendly towards Israel than Republicans. He is also seen (along, with many in the state department) as having staked so much on agreements reached with the former Israeli leadership, that he regarded the election of Netanyahu, albeit by the slimmest of majorities, as a disaster.
Now, though, even Mr Netanyahu is said to have come around to the view that Dennis Ross can be trusted - and that his experience is an advantage. However, whether that will be enough to make this make-or-break trip to the region a success, is not something anyone in the chancy business of Middle East diplomacy would stake his future on.