Is Bailout Constitutional?

According to our Constitution, all appropriation bills must start in the House of Reps. So, here is my question and thought. Is the bailout bill that started in the Senate Constitutional?

The original bailout bill was defeated in the House. The Senate essentially took a dead bill and revised it, so basically they created a new appropriations bill. The proper thing for the Senate to have done would to make suggestions to a House finance committed of proposed changes, and let the House revise and vote on the new bill first. So my contention is that this new bailout bill can be contested on Constitutional grounds. Of couse there is probably several loopholes that the Senate took advantage of, buy I cannot figure out what they could be.

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