I hear flanger but not much fuzz on the bass on that track, but I could be mishearing things through these unbassy laptop speakers.
I would guess a Big Muff and a phaser. The thing with Battlescar is that there are two bass tracks, if I'm not mistaken.
Definitely two bass parts. This is why the album version: Sounds very different from the live version: It was recorded along with RUSH. Two bass parts, two bassists. To unify both, a muff-like fuzz and some modulation would do the trick. The best would be to use a blender for it.
So he needs to split his signal and have modulation on one channel and fuzz on the other? Or fuzz and modulation on both channels and just a clean channel?
He could try either. I mean, he could do without the clean as well. But, getting the distorted in one channel and the modulated in the other channel might make it sound closer to the recording. Although, depends how much you care about it all. You could just get a fuzz at low to medium gain, send that into a flanger or phaser, make sure to EQ enough lows back in the signal, and call it a day.
If you look at the live version video, It sounds like it's all going through the modulation, maybe a bit of clean blend. But, hey, some people might play that song without no effects, or just with modulation, or just distortion, depends how close you want to get to the original. Also, OP did not mention if he wants to actually replicate the song's tone to play that song or he just likes that tone and wants to use it somewhere else in a slightly different way.
I believe the bassist was Dave Myles. In the intro you hear two separate bassists playing two different parts. The distorted bassist is Dave and the other bassist is, of course, Geddy. Once the song starts though, they do play in unison but Geddy gets some leeway in the song (especially during the guitar solos). Great track. I wish I could help the OP. I do know this was recorded in 1980 so whatever pedals were out there at that time are fair game. Good luck.
If we're talking about the first video that modulation is almost definitely Flange, not phase ~ or so my speakers have convinced me