I section hiked NoBo on the CDT this past summer from Rabbit Ears Pass to Canada, saw my first CDTers in Montana going SoBo. I didn't keep a count of everyone that I saw, but it was somewhere around 20. I heard from those on trail that there were more, one couple I believe, said that there were around 40 SoBo hikers. I may have missed others in the early mornings or evenings when one of us would have been in camp. I may have passed a few and not noticed them in the crowded Glacier NP, or when one of us was in town to resupply. Either way, there were plenty of other hikers that I saw and if you made an attempt I would think that you could quite easily find someone to hike with. There was a group of 5 I came across that was a group of 2 and 3 before meeting up and there was a group of 2 that were solo hikers. Then most people on the trail seemed to know roughly who was in front of them and who was behind them even though I was the first NoBo any of them had seen (many met in Glacier). So even though the CDT is a lot more remote than the PCT or AT the hikers I talked to seemed to be fairly well connected.
If I were you and really didn't want to hike without someone I would stop by the Many Glacier ranger station for permits. They will have information and most likely know people who have started and where the are. Most people keep a low to moderate pace through Glacier so you could probably catch someone who is a day ahead of you if you push. Or you could hang around the ranger station a day or two to wait for others to come by. Another option would be to get through Glacier then slow your pace, most people I ran across were doing 25 - 30 miles a day. Do half of that for a day or two and you will surely have someone catch you. Then obviously you need to start with the bubble, so just pay attention to the trail conditions, and watch the forums to see when most people plan on starting. What I understood from those I came across, nearly everyone started within two weeks from each other.
Hope this helps, the other responses had numbers so I figured I would give my experience. Ideally someone who hiked SoBo chimes in, but as I said, most people knew about others around them. As others have said, the CDT is continuously getting more popular (largely due to the Ley maps being on the PDF Maps app now). I wouldn't worry too much about hiking solo, just make sure you start with the pack. Keep an eye on the forums and I would be truly surprised if you have to hike alone for much time at all.