There is some inconsistency about whether, in the context of complexity analysis, an optimization problem is defined as asking for the optimal solution or the optimal objective function value. For example, Wikipedia's entry on decision problems says:
There are standard techniques for transforming function and optimization problems into decision problems. For example, in the traveling salesman problem, the optimization problem is to produce a tour with minimal weight. The associated decision problem is: for each $N$, to decide whether the graph has any tour with weight less than $N$. By repeatedly answering the decision problem, it is possible to find the minimal weight of a tour.
The second sentence defines the optimization problem as producing the optimal tour, whereas the last sentence implicitly defines it as producing the weight of the optimal tour.
Similarly, the entry on optimization problems says:
For example, if there is a graph $G$ which contains vertices $u$ and $v$, an optimization problem might be "find a path from $u$ to $v$ that uses the fewest edges". This problem might have an answer of, say, 4.
But 4 is not an "answer" to the problem of "find[ing] a path". So, this quote, too, is inconsistent about whether the optimization problem means finding the optimal solution or finding the optimal objective function value.
I am not trying to wade into a debate here about the quality of Wikipedia entries; I'm just trying to make the point that in common usage, there is an inconsistency about the way "optimization problem" is used, and that inconsistency can lead to confusion about the relationship between decision and optimization problems.
Now, back to your original question. If what you are asking is:
How can you reduce the "find the optimal solution" version of the optimization problem to the decision problem?
then I don't know of a way to do this, though @David Richerby gives one in his answer.
If what you are asking is:
How can you reduce the "find the optimal objective function" version of the optimization problem to the decision problem?
then the answer is, using binary search, as you have pointed out.
And if what you are really asking is:
Why does everyone say you can reduce the optimization problem to the decision problem, when it seems impossible?
then my answer is, when people say you can reduce the optimization problem to the decision problem, they mean the "find the optimal objective function" version of the optimization problem, but they are not always sufficiently clear in articulating that.
Now, from a practical perspective, if you are actually going to solve the decision problem, you usually run some algorithm that determines whether the items can be packed into $k$ bins. That algorithm is most likely going to do the packing, so in the course of your binary search, you will find the actual packings.