Determine which way to place beam for maximum strength

Yellow pages (or google, or...) and "Structural steel" (or structural steel suppliers, fabricators, erectors, etc.) Many may not really want to work with you (there's not really any classification of "suppliers of one beam for a house project" so some of the companies listed may ONLY play in the "build a skyscraper" market) but that's who you need for structural steel, and someone will supply residential one-offs, - ask for a recommendation if the company you call first can't help you directly.

Hiring the erection as well as fabrication and delivery is highly recommended. They know that they are doing and they have the right tools and equipment to do so safely. It's all too easy to kill yourself or your helpers when trying to creatively hoist heavy metal into place without experience and tooling for the job.

There are lots of span calculators available online, which help you determine what size lumber to use in home or deck construction. For example

http://www.awc.org/codes-standards/calculators-software/reversecalc

and

http://www.awc.org/codes-standards/calculators-software/spancalc

You could try to figure out what the live loads and dead loads for the bed are and go from there.

Shortcut - I might try to get by with 2x4's spaced 2' or less apart if they run side to side across a single mattress, but I'd want 2x6's if they run long ways, or for a full or larger.