We selected this bicycle after we had tried several times.
Does it mean that we have tried it several times and then we selected this bicycle (this bicycle is tried several times then bought) or we tried several bicycles and then selected this?
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As observed in comments, the structure is slightly odd. It doesn't include an object to the verb "try", and without an object, the usual meaning of "try" is "strive". But that meaning wouldn't make sense here: So we need to consider "pragmatics" understanding meaning based on context.
When the word try has an object it means "test". Consider the sentence
"We assembled the sofa after we had tried several times".
We know that assembling a sofa can be difficult, so we understand that "tried" means "tried assembling it". But "tried selecting it" doesn't make sense (since if you know what "it" is, it has already been selected.
It could be "several times" is the object. Compare
"we selected ice cream after we had tried several cakes".
But whereas I understand what "trying a cake" means. I don't understand, in this context what "trying a time" is.
Without the word "times" the meaning would be clear. In "after we had tried several.", the word several is a pronoun, referring to "several bikes".
It could mean "after we had tried it several times", with the object omitted but implied. This makes pragmatic sense, but the object would not normally be omitted here, precisely because it is ambiguous. This is the most likely meaning, yet it is not well expressed.
In conclusion, it's not a very good sentence. Of the several meanings but they either don't fit the context or could be expressed more clearly.