Just in case anybody else was having this same problem, I contacted MATLAB Technical Support and I was told that this was a bug on MATLAB's end that is being fixed in the next release(R2014b). They said that if you are having the problem I described in my original question, that in order to make the bar graph appear within the axes' boundaries at the moment, that you can edit the figure's 'Renderer' property and set it to either 'opengl' or 'zbuffer'. I have tested this and both options work so hopefully that helps :)
And just for extra clarification if it is needed, all I needed to change from my original code was:
mainFig = figure('Units','characters',...
'Position',[40 5 200 50],...
'Color',[100/255 145/255 209/255]);
To this:
mainFig = figure('Units','characters',...
'Renderer','opengl',...
'Position',[40 5 200 50],...
'Color',[100/255 145/255 209/255]);
And now the bar graph behaves as it should.