Ja bald vs bald
What is the difference between "ja bald" and "bald" alone in expressing an upcoming event? E.g. "Ich gehe bald nach Hause" or " Dann gehe ich ja bald nach Hause"
"Ja" only adds a slight increase in intensity to the statement; here, I interpret it as something like "you and I know". These elements are called "flavoring particles", and they are very common in German.
Dann gehe ich bald nach Hause. -- A neutral statement.
Dann gehe ich ja bald nach Hause. -- (We know that) I'll go home soon then.
Edit: Here's the Wikipedia article about these particles that are also called modal particles (but I find "flavoring" nicer ;-)) https://en.wikipedia.org/wiki/German_modal_particle
I would translate this ja modifier as after all in most cases, it reiterates on previously known or assumed knowledge. In other cases, sometimes it conveys surprise or indignation. It can mean a lot of things, but these are the most common ones.
Your example sounds pretty odd to me without context. It sounds like the speaker wants to remind someone they will be going home soon, and therefore something follows. (After all, I will be going home soon, so therefore...). Or the speaker could be surprised at how late it is already and they have to go home at a specific time (Then that means..., I will go home soon!)