The Queen has arrived in Ireland for a historic visit as it emerged that the Irish army was forced to make safe a viable improvised explosive device found on a bus.

The royal party touched down at an airstrip at Baldonnel, near Dublin, on Tuesday at the start of four-day visit – the first by a British monarch to the Republic of Ireland.

The bomb was discovered in the luggage compartment of the vehicle at a bus stop on the outskirts of Maynooth, in Co Kildare late on Monday night. An engineering unit from the Irish Defence Forces arrived at 11.10pm after receiving a request from the Garda Síochána.

An Irish military spokesman said a controlled explosion was carried out close to a hotel and the scene was declared safe at 1.55am. The remains of the device were handed over to the Gardai for investigation.

The bomb discovery comes after a dissident republican terror alert brought parts of London to a standstill on Monday.

Some opposition to the royal visit has been voiced as dissident republican violence rises. But both the British and Irish governments say they hope the official trip will hasten a new and better relationship between the people of Ireland and Britain, built on equality and mutual respect.

An unprecedented security operation, costing about €30m (£26.2m), is in place to safeguard the Queen and Prince Phillip. It includes land, air and sea patrols and a "ring of steel" around the centre of the Irish capital, where the main thoroughfare, O'Connell Street, has been closed to traffic.

The prime minister, David Cameron, will join the Queen on Wednesday for part of her trip, highlighting the importance of the visit, and the foreign secretary, William Hague, will accompany the royals throughout their stay, as part of normal practice.

The Irish president, Mary McAleese, interviewed by state broadcaster RTÉ for a documentary to be screened on Tuesday night, said: "I think it is an extraordinary moment in Irish history. A phenomenal sign and signal of the success of the peace process and absolutely the right moment for us to welcome on to Irish soil Her Majesty the Queen, the head of state of our immediate next-door neighbours, the people with whom we are forging a new future, a future very, very different from the past, on very different terms from the past and I think that visit will send the message that we are, both jurisdictions, determined to make the future a much, much better place."

The taoiseach, Enda Kenny, has said the Queen will receive a warm welcome from the Irish people, who would have opportunities to meet her. The royal tour will take in Dublin and the counties of Cork, Kildare and Tipperary.

In Dublin, the Queen will visit several politically and historically significant sites, such as Croke Park, the scene of a massacre by British troops, and the Garden of Remembrance, which honours those who fought for Irish freedom. She will also be guest of honour at events at Trinity College, the National War Memorial Gardens in Islandbridge, and the Guinness storehouse. Cork and Cashel are also on the agenda, along with a private visit to Coolmore, an international thoroughbred racehorse stud in Tipperary.

The Queen's grandfather George V was the last reigning monarch to visit the republic in 1911 when it was still part of Britain. The bitterness caused by the partition of the island a decade later and the use of the British army in Northern Ireland strained relations for much of the 20th century. But the success of the peace process has eased tensions and a visit by the monarch is seen by many as cementing a closer relationship.

The Sinn Féin president, Gerry Adams, stressed his party was still against the royal visit and would host celebrations of republicanism in each city the Queen visits. He described the tour as premature and insensitive.

Anti-war campaigners and leftwing republican group Éirígí, which has one council seat, are planning a series of protests.

The start of the visit falls on the anniversary of atrocities that claimed the greatest loss of life in a single day of the Troubles. Thirty-four men, women and children, including an unborn baby, were killed in no-warning explosions in Dublin and Monaghan on 17 May 1974.

The victims' families and survivors of a series of bombs have written an open letter to the Queen to mark her arrival in Ireland and will hold their annual wreath-laying ceremony a few hundred metres from where the Queen will commemorate Irish rebels in the Garden of Remembrance.

Justice for the Forgotten has appealed to the monarch to urge Cameron to open secret files which were withheld by the British government during an inquiry.