First, the phrase is 'to bode well/ill for '; I have never seen it with 'with'. COCA supplies 265 examples of 'bode well for' but only one example of 'bode well for'. It is a rather old-fashioned phrase and hence often a jocular or literary term little used in everyday conversation or writing.
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...when I Google searched for "bodes well with", the search engine came up with over 600,000 hits. Including the following example:"Future of tournament bodes well with early exits from stars" http://www.dailymail.com/Sports/201107311466