Let us apply the 4Ws:

• What happened? Train first started crossing Platform-Bob. Train then finished crossing Platform-Bob.
• Who was watching? Train-Bob and Platform-Bob. Let us call the events $E_1$ and $E_2$ on the train reference frame, and $E'_1$ and $E'_2$ on the platform reference frame.
• Where did they happen? $E_1$ occurs at the leading end of the train. $E_2$ occurs at the lagging end of the train. Both $E'_1$ and $E'_2$ occur right in front of Platform-Bob.
• When did they happen? At a time interval required by the train to travel its own length at the relative velocity $v$.

Let us say Train-Bob measures the proper length (length in its own reference frame) of the train as $l'$.

Now consider the length of the train as measured by Platform Bob. At the outset, we are not sure that this will be same as $l'$. So let us call it $l$.

Let $t$ be the time it takes for the train to pass Platform-Bob (as measured on the platform). Due to time dilation, this is measured as $t' = \gamma{t}$ from the train.

As the relative velocity is $v$ for both observers, $l' = vt'$ and $l = vt$.

As $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$, it is greater than 1 for $v < c$.

So $l < l'$ i.e. length of the train as measured by Platform-Bob is less than its proper length, measured on the train. Note that there is no contraction in directions perpendicular to the motion.

Set the ratio of $c/v$ to 1 in the gedanken, to observe what happens when the train moves at the speed of light!