Change the resolutions to match. Also, depending on the items included in the bitmap, you may want to move and resize a window during recording so that any windows are guaranteed to be of the same coordinates for position and size, regardless of the machine.
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I have heard that different video card drivers, different video card chipsets (as in Ati rage, or S3, or ESS etc...) may capture the bitmap in a different way. Resulting in your test failing in the other machine where the BMP was not captured.
How to avoid, simply do not use BMP checkpoints unless you are really, totally out of options.