What is the difference between "making a bid for freedom" and "making a break for freedom"? In which situations would one use one and not the other?
In the context you're referencing, a bid is
an attempt or effort to achieve something
whereas a break is
• a rush or dash in a particular direction, esp. by an attacking player or team : he made a bounce pass for a basket on the break in the second quarter.
• a breakout, esp. from prison.
The distinction is that a bid may or may not risk anything, whereas a break often risks much or all.
[References from NOAD]