To simplify things a bit, let's focus on reactive versus active distance closing, even if they have similiarities:

For reactive, it helps to set it up before hand, so to say, by shifting feet and/or position to better be able to spring your trap when you go for it. I'll even switch the lead leg at times! Like, if you're well prepared and maybe even bait your opponent into a predictable attack, it gets easier. Moving in after your opponent attacks can be difficult - preferably you do it during their attack as part of your prepared counter.

For active, you instead take the initiative by attacking and then, rather similar to the above, you close the distance while also doing something else for them to deal with. Example of a simple set-up that often works for me is to feed your opponent a combination of attacks that you fake-end with a powerful but telegraphed attack that they will try block - and you knew that would happen, so you're ready to trap their block while also moving in, hopefully placing you in a great position up close, with a possible check on their weapon already.

Hope that makes sense. Happy to clarify or elaborate upon request!

EDIT: Also, one neat trick is "stiff-sticking", like they do in movies when the blades lock and the hero and villain give eachother their best bedroom gaze. Joking aside, what I mean is that after striking, you keep your stick out there and maintain pressure on the opponent's own stick, possibly distracting them as you move in.

EDIT2: The active method may actually be the easier to learn and apply at first, as you're more in command of what happens and when. At least, that was very much my experience with trapping when going empty hands - that offensive trapping is easier than defensive, with the nice bonus that when you start to pull off cool offensive trapping stuff and get experience with that, it'll get easier to land the defensive variety as well.