Q:

Why did Robb not pursue alternative ways of crossing the river in "Baelor"?

In the "Baelor" episode of Game of Thrones, I was confused when the Starks had to negotiate with the Frey clan in order to cross the river. Was there no other way across the river? Did they not have boats or enough resources to quickly build a bridge?
Is this explained better in the books?

A:

Here's a closeup map of the Riverlands. Robb Stark's host was moving south from the Grey water Watch (mislabeled in the image) which is at the very top of map. They needed to go South towards Riverrun, which is the House Tully seat being besieged by Jaime Lannister (very bottom of the map). To do that they needed to cross the Green Fork, which was flooding at the time, so the only way to cross was to use the bridge spanning the Twins or go much farther south along the river, exposing them to Lannister troops and wasting valuable time. Hence the need to negotiate with Lord Walder Frey.
Relevant book passage (pp. 640-641 in my paperback copy in a Catelyn chapter):

Theon shook his head. "The river's running high and fast. Ser Brynden says it can't be forded, not this far north"
"I must have that crossing!" Robb declared, fuming. "Oh, our horses might be able to swim the river, I suppose, but not with armored men on their backs. We'd need to build rafts to pole our steel across, helms and mail and lances, and we don't have the trees for that. Or the time. Lord Typwin is marching north..." He balled his hand into a fist.
"Lord Frey would be a fool to try and bar our way," Theon Greyjoy said with his customary easy confidence. "We have five times his numbers. You can take the Twins if you need to, Robb."
"Not easily," Catelyn warned them, "and not in time. While you were mounting your siege, Tywin Lannister would bring up his host and assault you from the rear"

A:

Sorry about the sheer length of this, but Westeros is very long in the North/South direction.  Essentially, for a large army to go from the north (where Winterfell is), to the south (where King's Landing is), you need to:

Travel through a forest to the west.
Cross a large river.
Head to the sea up North, and sail the Narrow Sea down to King's Landing.

The middle option is apparently the best option.

Note: The Twins are in the middle of the map, slightly to the west.  Also, I haven't read the books, so I'm unaware of any mitigating circumstances.  I assume the forest to the west of the Twins is dangerous or somehow not worth the extra time to traverse it.

A:

Also don't forget that the idea was to separate Jaime Lannister's forces from Tywinn Lannister's army.  By cutting across the river, Robb Stark was able to move into a strategic position that would leverage position to counter inferior numbers.

