I would not get too worried about the likelihood factor here.
Even though the backshift occurs, the likelihood remains that of the
original tenses.
But on another point, there is something unidiomatic about the example
itself. It doesn't seem that that last sentence comes up very
naturally there. It seems to be floating with respect to time and
needs a preceding main clause to anchor it.
Also, from the viewpoint of logic, you were walking, so you didn't have
your bike. I'm confused about how you would show Mary your bike
if you didn't have it there.
Personally, I find the following more idiomatic and logical.
As I was walking around the neighborhood yesterday, I ran into
John. He told me that Mary usually walked her dog at about that
time. I [resolved / decided / told him] that if I saw her, I
would ask her if she wanted to see my new bike.
Maybe we can come up with a different example where the bare
conditional stucture comes up quite naturally in a past tense context without an introductory clause, but I
can't think of one just now.
CJ