This was plain reading.

She would at first have distrusted me, apprehending I know not what rashness of ill-timed and forever impossible declarations.

As she perceived this alarm to be baseless, for I not only refrained from intruding but I ostentatiously let Miss Kate alone, shyness would creep into her apprehension to make amends for its first crude manifestations.
As the days went by and I displayed still the fine sense to keep myself aloof, to seek Miss Kate only in those ways that I sought her refreshing mother, she let me discern more clearly her faith in my firmness and good sense.

To be plain, in reward for letting her alone, she did not let me alone.

And this reward I accepted becomingly, with a resolve--the metal of which I hoped she would divine--never to show myself undeserving of its benisons.
When I say that the young woman did not let me alone, I mean that she seemed almost to put herself in my way; not obviously, true enough, but in a degree palpable enough to one who had observed her first almost shrinking alarm.