The FogBugz XML API can get you what you're looking for via the listIntervals
command in the Time Tracking section:
cmd=listIntervals - returns all TimeIntervals for a user. Any of the optional arguments serve to filter the results.
Arguments
- ixPerson (optional) - Specifies which user's intervals should be returned. If omitted, list intervals for the logged on user. If set to 1, list intervals for all users. Note that you must be an administrator to see time interval information for users other than the logged on user.
- ixBug (optional) - Specifies that only intervals associated with this bug should be returned.
- dtStart, dtEnd (optional) - If dtStart and/or dtEnd are supplied, listIntervals will return intervals whose start date falls between dtStart and dtEnd.
So the query you'd be using would look something like this:
[your FogBugz url]/api.asp?token=[your XML API token]&cmd=listIntervals&ixPerson=[ixPerson you're interested in]&dtStart=[start date]&dtEnd=[end date]
For future reference, there is a FogBugz-specific Q&A site: http://fogbugz.stackexchange.com