The long-distance transport of messenger RNAs (mRNAs) has been shown to be important for several developmental processes in plants. A popular method for identifying travelling mRNAs is to perform RNA-Seq on grafted plants. This approach depends on the ability to correctly assign sequenced mRNAs to the genetic background from which they originated. The assignment is often based on the identification of single-nucleotide polymorphisms (SNPs) between otherwise identical sequences. A major challenge is therefore to distinguish SNPs from sequencing errors. Here, we show how Bayes factors can be computed analytically using RNA-Seq data over all the SNPs in an mRNA. We used simulations to evaluate the performance of the proposed framework and demonstrate how Bayes factors accurately identify graft-mobile transcripts. The comparison with other detection methods using simulated data shows how not taking the variability in read depth, error rates and multiple SNPs per transcript into account can lead to incorrect classification. Our results suggest experimental design criteria for successful graft-mobile mRNA detection and show the pitfalls of filtering for sequencing errors or focusing on single SNPs within an mRNA.