A bai file isn't an indexed form of a bam - it's a companion to your bam that contains the index.
A bam file is a binary blob that stores all of your aligned sequence data. You can view what's in the bam file using "samtools view bamfile.bam | less".
Bam files can also have a companion file, called an index file. This file has the same name, suffixed with .bai. This file acts like an external table of contents, and allows programs to jump directly to specific parts of the bam file without reading through all of the sequences. Without the corresponding bam file, your bai file is useless, since it doesn't actually contain any sequence data.
If you have a bam file without a corresponding index, you can generate one using "samtools index bamfile.bam".
If your index file is named identically, with just the additional ".bai" suffix, you can be reasonably sure that it was generated from the same file. If you have any doubt, though, it's easy enough to delete your bai file, then generate a new index using the previous command. Keep in mind that this may take a half hour or more depending on the size of your bam and the speed of your computer.