If the number of votes to impeach reaches 67, the constitutionally required number, Bush's only option may be to pull a Nixon and resign, asking Cheney to resign first and appointing a Vice President under the provisions of the 25th Amendment. The ball would then be in the Speaker's court. If she decides that the nation has had enough Republican rule, she could block it. In 1974, Speaker Carl Albert was not fit for the presidency due to his rumored taste for the grape. This is not the case with the current Speaker. If she wants the presidency, she could easily block any nomination provided the votes for impeachment are in hand.
Of course, the votes may not be in hand if she is seen as blocking the appointment of a Republican successor. It all depends on the popular pressure for impeachment. If it is irresistable, she could opt to be President. This would force the current crop of contenders to demure if she desired to run for the seat in her own right. If she offers the Vice Presidency to the junior Senator from New York or the junior Senator from Illinois, the die will be cast for the given future in the Democratic Party.
On the Republican side, being summarily tossed out of office would not bode well for any nominee. An appointed President would likely not fare too well either, especially if a challenger remained in the party or if a pardon were given for ordering torture - although such a pardon would not stop an action by the Hague.
In either case, the door would be wide open for a Michael Bloomberg candidacy. If a percentage of the people believe the Speaker stole the presidency, he would benefit from any backlash. He would also likely beat any appointed President, although in that case Mrs. Clinton would likely pull in the most votes, although possibly not an Electoral College win.
In this case, the Presidency would depend on who wins the most states in the House. Note that the Draft Bloomberg Committee is aggressively recruiting such candidates. If 26 states cannot be lined up, whatever coalition is put together in the Senate may lead to the election of a Vice President. Under this circumstance, whoever is named Vice President by Mrs. Pelosi or the appointed GOP President may or may not have the deciding vote. That could very well be Mrs. Clinton, who could then elect herself President.