Much depends on which Juco you're at. It also depends on if you are "extremely" talented or you have a team mate who will draw scouting attention.
DI coaches can't get out to lots of Juco games for obvious reasons. However, MLB scouts know about the most talented Juco players (especially the ones at good Jucos) in their area and they do follow those players very closely because they are all eligible for the draft.
What all this means is that the pro scouts are often a players best promoters for 4 year schools. If you are a good prospect and playing at any competitive Juco, the pro scouts will know who you are. They might like you a lot, but think you need another year or two. Most pro scouts have good relationships with many colleges. After all, they need to work with those colleges.
It's possible that a good Juco player would have to promote or market himself to other colleges. But in most cases, when a player has enough talent the Juco coaching staff and MLB scouts will be your surest ticket to the next level.
As far as DI goes, making contacts on your own make sense if you are already being recruited by other DI colleges. If you're from Iowa and you contact LSU, they will want to know if Iowa wants you. I know that is an extreme example, but the point is if you're a Juco player that stands out, people will know about it. If you're not a Juco stand out and looking for a small college opportunity, by all means, you need to start contacting schools.
This is just my opinion, TIFWIW. For sure I would ask my Juco coach what he thinks might be the highest level you should seek. That will at least tell you what he thinks. What he thinks is going to be very important because whoever you contact is likely to end up talking to him. And if you are the DI coach, whose information carries more weight, the player or the coach?
Just remember, if you're at the right juco and have enough talent, chances are you have nothing to worry about. If you happen to be at the wrong Juco and have the talent, but feel you're getting overlooked... Get busy!
One warning: Some Juco coaches have close ties to a particular college. Most of their top players end up going to that college. Sometimes the Juco coach is that colleges best recruiter. So if looking for lots of options, unless that option is satisfactory, you might think twice before heading off to that Juco.