The US says the shield is to protect against states such as Iran and North Korea, but the move has angered Russia which sees the system as a threat.
Bush again played down Moscow's concerns about the missile shield, saying: "This system is not aimed at Russia. I will continue to work with President [Vladimir] Putin and give him those assurances as well."
Washington wants to put base 10 'interceptor' missiles in Poland and a radar station in the Czech Republic as part of the system.
The US and the Czech Republic are close to finalising an agreement, but the Polish government has taken a tougher stance in negotiations and many details remain to be settled.
Bush has visited Poland three times in his seven years as US president, a measure of his appreciation for Warsaw's steady pro-American stance underlined by the hundreds of Polish troops who have served - and in two dozen cases - died in Iraq.
But that alliance has undergone a serious reassessment since last October when Polish voters threw out the conservative government.
The new government led by Tusk has announced that all Polish forces will be out of Iraq later this year.
Tusk said Poland was ready to co-operate on missile defence as part of a security effort that would include the upgrading of Polish forces.
But he has put Washington on notice not to expect quick or easy approval of its missile plan.
"I understand that America cares about its own security and I share the opinion that the security of America effects global security," he said.
"But Poland lies in a specific location and has a very specific history which means that we need to seriously consider concrete, and measured aspects of security when it comes to such critical events in the region."
Bush admitted "there's a lot of work to do because many times a strategy on paper is a little different from the details so our experts are working through the system to make sure the people of Poland are comfortable with the idea".
But he promised that "before my watch is over, we will have come up with a modernisation plan that is concrete and tangible", referring to the end of his period in office in January.
Polish officials have said they want to acquire air defences against short and medium-range missiles.
Negotiators have asked for Patriot 3 or THAAD missiles and have identified 17 areas of the Polish military that the US could help modernise.
The interceptors for the planned US shield are for protection against long-range missiles.
The Polish government says that the security backing is necessary because Russia has threatened to target Poland with nuclear missiles if it allows the interceptors to be based there.
The Poles have also said they are wary that they could pay a heavy political price if a Democratic president succeeds Bush and decides to abandon his European missile shield concept.