With JIRA, there are features that allow you to Start Progress and Stop Progress on an issue or various issues at any given time. Is there a way for me to go back and see a chart or a graphical representation of how my time was spent over a set period of time?
If I wanted to see how many bugs I worked on in April, and see how much time (graphically) was spent on each bug, could that be done, and if so, which version of JIRA would allow me to do that?
I dont think you can see for a given month how much time was spend on a task. You can see how much time was spent on a task, but not what time period it was for.
I'm sure you've already seen this: http://www.atlassian.com/software/jira/docs/v3.13.3/timetracking_report.html
There's a Time Sheet Summary report that comes with the Timesheet Report and Portlet plugin - it shows you a list of the JIRA issues you've been working on together with the time per day for a configurable period. No charts, though, I'm afraid.
I think in general that time tracking is ripe for someone to write a really good JIRA plugin; I'm not totally happy with any of the current ones.