Immediate cap savings
The Lions' move to release Bush freed up $1.72 million in cap space. The Lions could have created $3.5 million in cap room by making Bush a June 1 cut, but they would have had to wait until that date to actually make use of that extra space. Considering they may need every penny available to franchise Ndamukong Suh in the next few days, I suppose this was a case where it made sense to be impatient. And even if the Lions don't franchise Suh, that $1.72 million could come in handy for signing him to a long-term extension, and it could also be used to sign other free agents.
More playing time for Theo Riddick
The Lions will almost certainly add a running back or two this offseason (more on that in a second), but this move indicates that they have a lot of confidence in Riddick. Riddick received a lot of hype last offseason, but his playing time was still quite limited more often than not in 2014. Actually, it was quite frustrating to see Riddick consistently end up on the bench in favor of Bush even though Riddick looked more impressive. Riddick definitely has work to do as a traditional running back, but he is quite good in the passing game, and Bush's exit should create more opportunities for him going forward.
An increased need to draft a running back
You could do a lot worse than a one-two punch of Joique Bell and Riddick at running back, especially when you throw George Winn into the mix as well. However, there was talk of the Lions drafting a running back even before Bush was released, and now it seems like something they will almost certainly do. There are no guarantees, of course, but general manager Martin Mayhew hasn't shied away from drafting running backs in the past, especially early in the draft:
2009: Aaron Brown (TCU), sixth round (192nd overall)
2010: Jahvid Best (California), first round (30th overall)
2011: Mikel Leshoure (Illinois), second round (57th overall)
2013: Theo Riddick (Notre Dame), sixth round (199th overall)
The Best and Leshoure picks didn't exactly work out, although injuries were as much to blame as anything. Even so, it will be interesting to see how the Lions approach the draft this year considering how deep the running back class is. It's entirely possible that they could have a shot at the top running back in the draft with the 23rd overall pick, but waiting until the second or third round to address this position might make more sense.
Of course, I suppose we shouldn't rule out the possibility of the Lions pursuing a running back in free agency. Justin Forsett has already been mentioned as a possibility, and it seems like the Lions could get pretty good value depending on who they target. I can't imagine they will make a run at a big name like DeMarco Murray or Adrian Peterson (if he's available), but that second or third tier of running backs always seems to produce a player who signs for cheap and then goes on to put up some good numbers. Going this route would give the Lions some extra depth and still allow them to explore the possibility of adding another running back in the draft.