You often see this with different mappers, and it really depends on the settings that you've used for the mapping itself. In other words, what did you do to generate the .bam? I assembled some mitochondrial genomes several years ago using a mapping/consensus approach in Bowtie2 much the same way you are doing, and I noticed that the 'quality' of the final result depends on whether reads were soft-clipped or not either using --local or --end-to-end. Remember that you're basically stacking up your reads on your reference, and how many reads stack and where depends on your settings.

I'm going to give a shameless plug here and recommend Assembly by Reduced Complexity (ARC), a project that I am involved with that is currently available. It does a better job than all existing applications (that I am aware of) of iteratively assembling sequences starting from a (possibly very divergent) reference in a parallel fashion. It does an amazing job with circular genomes like yours, too, requiring little or no trimming of overlapping circular ends after the fact. I used it to assemble ~60 chipmunk mitochondrial genomes starting from the squirrel (and it works with monotremes and marsupials, too!) with high accuracy and effectively no reference bias. In contrast, Bowtie2/samtools introduced Ns at the ends or internally where there was a dip in coverage, just like you are seeing.

Another, less accurate option is to do a de novo assembly using, say, Newbler and BLAST the contigs to your reference. This is more computationally and informatically intensive.