From my experience (as someone who is finish up his master's degree) it is best to get a masters degree. During your master's degree there will be room for an internship so you get both. Also make sure to choose courses relevant to the game industry (like graphics, geometric algebra, calculus, etc...).
This is because unfortunately game industry related bachelors are 'tainted' these programmes have been creeping up everywhere and usually do not contain the knowledge at all that you need to program games. For example not much of these programmes include advanced calculus and linear algebra courses while most do include some sort of silly gamemake based course. Guess which of these two courses will come more in handy when you're trying to find an efficient algorithm to compute vision metric over a complicated graph structure ;).
Added bonus: people with a master's in CS are very scarce (at least here in the EU) so if you have a hard time finding a game related job you have a very easy time finding something else (that will probably pay a lot better ;) )
Sources: me and people I talked to at Nixxes (Tomb Raider) and Abbey Games (Reus) where I did internships) and Crytek where I had an in-house day.
Edit: the opinions here differ a lot. So why not call up a few of your favorite game companies and ask them what they think? Just find their phone number (best) or e-mail address (really only if you cant contact them by phone). Most HR people are actually quite nice and will love to give you some short advice.