There's not enough data for any trend to be clear.
You found ~26 bugs in the last half of May. You found ~27 bugs in the first half of June. If the bug discovery rate keeps going like this, you're projected to maybe find 40 bugs in the month of June (40 being somewhat conservative).
So you have potentially two data points: 26 and 40.
Consider this hypothetical situation:
July: 37 bugs
August: 46 bugs
September: 33 bugs
October: 33 bugs
November: 29 bugs
December: 17 bugs
January: 25 bugs
February: 24 bugs
March: 19 bugs
April: 18 bugs
May: 14 bugs
Put that in your favorite spreadsheet app and plot it as a bar graph. Look familiar? If your upper management is trying to find some significant progress on the order of 160 hours of work by one tester, they're sorely mistaken. What you need to show management is that you've already identified 43 bugs in the code while implementing this new workflow/tool/testing technique.
It may be that you're in the hump on the left of their 'expected' outcome. It could also be that 1 tester on 1 project isn't enough to generate that kind of pattern at all. In fact, if bug finding remains constant, that means you don't have enough people testing in order for them to find the bugs fast enough; eg by the time they find 20 bugs, another 20 have been created and are waiting to be found. The only way to see that downward trend as time goes on is if your testers are able to find bugs faster than they're created.
Just try to emphasize that this is a problem whether it's recorded or not, and that there isn't enough data to come to any sort of conclusion yet. If they seem like they want to get rid of that position or stop testing altogether, try to get them to see this as a probationary period and try to convince them to give your team 6 months to try it out, and even go so far to schedule a date/meeting where the results of the probationary period are presented.
So to summarize:
Emphasize the small data set.
Try to get testing extended to at least 6 months
Present results at the end of the 6 months, and try to justify the benefits received from testing
Emphasize these bugs exist whether they're recorded or not, and bugs in code are potentially very expensive risks.