Here are some ideas but I off the top my head that just may work...
If you take your array and subtract the elements from each other to get an array of one less points, but that's the first derivative. If you now smooth that and look for the sign change, that may detect your bump.
Perhaps using 2 lagged (exponential or windowed) moving averages might reveal the large bump while ignoring the small one. Basically, the width of the smaller window moving average must be greater than the width of of the bumps you want to ignore. The wider EMA must be wider but not too wide to detect the bump.
You look for when they cross and subtract the lag (window/2) and that's an estimate where your bump is.
Do a series of linear models of sufficient width that are several little bumps wide, let's say 100 points. Now loop thru the data set generating linear regressions on the X variable. Just look at the coefficient of X and see where the big sign change happened. That is a big bump.
The above is just conjecture is on my part and there are probably better ways of doing it.