Dreamworks issued a press release today indicating Thomas Newman will score Bridge of Spies. The press release simultaneously confirms that Williams will score Spielberg's The BFG.
http://blogs.indiewire.com/theplaylist/thomas-newman-to-score-steven-spielbergs-bridge-of-spies-john-williams-will-tune-up-the-bfg-20150318
I tried to notate and play the piano melody from 10:41. It's very rough (and I will probably regret doing this when the actual OST comes out...there are likely to be inaccuracies!) but I think I got at least the basic melody line down:
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No need to mention that this is 100% Williams. The planing chords are very reminiscent to those of A.I for instance, and the beginning of the melody is reminiscent of Lincoln's "With Malice