There are 2 train companies operating 2 routes - MML, Cross Country. The cheapest train costs $65 and is 2h 43min.
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There are 3 ways to travel from Bedford to Leeds. 4 buses, 1 train and 1 by car are possible between the two areas. The by car from Bedford to Leeds is the cheapest. The train from Kempston to Morley is the fastest. The train operated by running from Bedford to Leeds is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!