An extension of Metrolink from Bury taking over the ELR seems very unlikely. I'd estimate the probability of an extension directly north from the existing Bury station as zero - it would require a tunnel being bored under Bury town centre to rejoin the line north of the Bury Bolton Street ELR station, it's a complete non-starter.
The alternative would be to bypass Bury station - the junction between the Metrolink line and the ELR is
here [google maps link] - and convert Bolton Street station into a Metrolink stop. Which is possible but it's not a great location within Bury for a station, it's right on the other side of the town from the new shopping centre. The stretch of line between the junction and Bolton Street station doesn't look like it's in a great state from the overhead view, but it must be better than I thought as the ELR is providing traction for Metrolink engineering trains I suppose. It does go over
a level crossing though - would reintroducing an old level crossing (it was on the Bury-Manchester line before that was redirected into the current station) into regular reuse be acceptable? That said, the road it crosses is very minor, in bad condition and I suspect would be a strong candidate for closure were it a railway line.
It's a nice idea, but I can't really see a sensible way of doing it within the existing infrastructure.