Since there are no replies yet, here's my best take on a suitable route. I haven't ridden all of it, though: only the High St, Capital City Trail and Sandridge Trail sections. It goes something like this:
From Bulleen, go down Bulleen Rd or Thomsons Rd (depending on exactly where your mate's coming from, I guess), cross the freeway, then continue along Bulleen Rd, then take Doncaster Rd, High St, and Church St. Turn right from Church St onto Bridge Rd, left onto Burnley St, then you should be able to join the Capital City Trail somewhere around that point (I haven't ridden this road, so don't know exactly where he would join the trail). Follow the CCT along the Yarra's north bank to Melbourne, and continue following it along the Yarra's north bank until you get to the Spencer St bridge at the west end of the CBD. Go south over the bridge, then turn right to ride along the start of the Sandridge Trail. This starts where Normanby Rd heads southwest from Spencer St. Follow the Sandridge Trail to its end, which is Port Melbourne.
Note: I find High St reasonably OK to ride along, although I head northeast along it in the afternoons, and only between Studley Park Rd and Belford Rd. The usual cautions apply, of course, for any of these sections: keep an eye out for motorists who may without warning turn left/right entering/leaving the road you're riding on.
Regarding your comment on the Koonung Trail: this turns south off the Yarra Trail just east of Burke Rd, runs under the freeway, and then heads east, so it's usefulness to your friend in commuting is limited (in my opinion, anyway).
Hope this helps