Hi again Casey and more welcome! More little forum tips -- I took the liberty of moving this post from where you had put it (organic insect and plant disease control) to the bonsai forum, where our bonsai experts are more likely to see it. Maybe the mold qualifies as plant disease, but I think most important is you have a new bonsai and a lot of questions about it. So along with good titling, trying to post your questions in the most relevant section helps too.
I'm not a bonsai grower, I just read our forum a lot. From that I would suggest that whether or not watering every day is too much depends on your tree, your growing medium / soil and other factors. You want to submerge it, then let all the water drain out and then not water again until the top part of the soil has dried out again.
I will be interested to see what the bonsai growers say about whether you should leave that moss there. It seems to me like it would hold too much moisture and make it more difficult to tell whether your soil is drying out or not... but I do see pictures of bonsai with moss, so maybe it is all right.
While we are waiting for the real bonsai folks to come along, help them out by telling us a little more about the conditions you have your new juniper bonsai in-- indoors/outdoors, what kind of light, what is the soil like, etc.
Best Wishes with it!