Here's some philosophy on lip slurs. I haven't played this book in particular, but as a brass specialist I can talk about lip flexibility in general; it's the same thing.
The ultimate goal of this is to have a clean transition between any two notes in different partials. This is the same whether you are trilling between two partials in a high register very quickly or jumping over many partials in the middle register.
I'm curious as to what you mean by "bending." This might just be a shorthand for a different notation, or a misinterpretation of some marking, but I can't think of a situation outside of jazz or modern extended techniques where you would need to "bend" a note on the trumpet. Trills do not require that.
What is being shown in this example is a pretty simple lip slur exercise. The notation indicates that every pair of notes should be tongued, slurring from the first to the second note of each pair with a continuous airstream.
One way to practice this at first would be to play on the mouthpiece alone by slowly glissing, or bending, from the first note to the next. This helps to encourage the right lip movement and continuous airstream. As this starts to feel comfortable you can speed it up, so that when you put the mouthpiece back into the instrument, the movement is so fast that you only play two pitches and don't hear anything in between. That's the objective, a clean, clear break between the G and the C.
The idea is to make the lip slur sound no different from a slur between two notes in the same partial with different fingerings. You can play two different notes in the same partial just by depressing a valve; this will give you a clean, clear break between the two notes, and they will be connected if you don't interrupt the airstream. Your goal is to make two notes in different partials with the same valve combination under a slur sound exactly the same way.
As you get to more advanced material, you will extend this by beginning to lip slur across partials. Consider a 6th between middle G and high E. Both of those notes are played open, but there is a partial in the middle for high C. When you slur between G and E, it should sound no different than slurring between G and C (and by extension, no different from playing two notes right next to each other with valves). When you first try this, you will almost certainly hear the C in between those two notes (because keep in mind, you shouldn't use the tongue to articulate a lip slur!). Your job is to minimize that partial in the middle to the point where it disappears entirely and you only hear the G and E when you slur between them. This is why practicing lip slurs is so important to brass players--it's our life blood.
Lip trills are just these techniques taken to their extreme in the upper register. You're going to start practicing them VERY SLOWLY, and should be aiming for the exact same kind of lip slur that you're practicing now: clean, clear breaks between notes. The only thing different is that lip slurs happen in the very high registers, where partials are only 1-2.5 semitones apart, and the slur is going to happen very fast.