For others running into the "Speitz" pronunciation issue: I did some digging because I was absolutely sure I was not hearing "Bett." According to a dev in the other thread it's a known issue with the way some computers are interpreting the audio. It has, however, been two years since they became aware, so, unfortunately, it looks like we'll just have to grin and bear this one.
Just so you're not all going crazy like me, she is saying it incorrectly for some and not others, at least for the time being.
Generally, with prepositions of position (über, auf, an, in, vor, neben, unter, hinter, zwischen.) it will go dative when referring to position, and accusative when referring to movement.
Ich gehe ins Bett = accusative: I am going into bed, moving to it. Ich sitze auf dem Bett = dative: It's my position, where I am.
Here are two examples with "movement", but one implies movement toward, one implies a position: If I say 'Ich laufe in die Stadt' (accusative), I mean I am walking into the city (direction). 'Ich laufe in der Stadt' (dative) suggests I am walking around within the city (going around downtown, for example). Even though the second sentence contains movement, my position remains within the city.
'ins (in das)' is in the accusative case, and will be used where movement (you are going into bed) is involved. 'im (in dem)' is in the dative case, and will be used when talking about position (you are in the bed). If I'm walking into a room, I'm going 'ins Zimmer', but if I'm sitting in class, I'm 'in dem (im) Zimmer'.
In my studies I have observed that in German you often use, and even need, the article far more often than you do in English.
This particular example is interesting as we say (in English) that we "go to bed." If we translate that word-for-word into German it would seem like we're going up to the bed, but without getting in/on to the bed, and German would require the article. Even if I say I'm getting into bed (under the covers) English requires no article for the bed in question unless it's some specific or non-typical bed (like, not yours).
Generally, in German, count on using an article, even if you wouldn't need it in English.