Published empirical data on this point is surprisingly rare, and people generally report numbers without providing a hard citation. The general argument is that steric constraints imposed by the ~10 bp helical twist of DNA constrain a single TF binding domain to access the major groove over stretches of DNA <10 bp. TFBSs with >10 bp binding sites are typically due to homo- or hetero-multimers, or to TFs with >1 DNA binding domain. To answer your question directly, using ~400 TFBS that are literature curated from small-scale studies (e.g no ChIP-seq or Chip-chip) based on DNAse footprinting, gel shift, etc. in the ORegAnno database, leads to an estimate of 11.9 bp. A quick double check of this value would be appreciated.

The length of DNA binding sites of individual transcription factors tends to be in the region of 6-10 bp, and that doesn't very all that much between say fly and human, as a lot of the TF DNA binding domains are highly conserved. The length will vary depending on the specific transcription factor family you're looking at - for some of them, X-ray crystallography structures have been published, you can look these up for binding site lengths. Motifs aren't necessarily a true reflection of the exact length of binding sites, as they are computationally derived from the sequence, rather than experimentally determined.