I hope you don`t mind taking the opinion and thoughts of a rank ameuter,my friend...
Even though I can`t (as yet)play most of the songs with those incredible basslines that just make us all go *said under one`s breath* "Damn.DAMN.
DAMN!! " I can still recognize a super chunky and powerful bassline in a given tune. No comment on the bass solos things here. I guess they are cool depending on the situation at hand.
How about some really,really solid and active basslines?(ala RHCP). What just floors me about the well-written bassline is how it can almost play counter to the melody/guitar/vocals by nice fills and variations on the song`s beat and rhythm.

Not sure I`m a `splainIN right,Lucy.
...how about these?
"No Such Thing" - John Mayer (phenominal bassline,IMHO)
"All I Want" - Toad the Wet Sprocket (makes this pop-ballad bassalicious)
"Year of the Cat" - Al Stewart (simple and sweet...but movin`!)
"From the Beginning" -Emerson,Lake & Palmer (original accoustic is my fav but...hard rockin`electric version?)
"Don`t Dream It`s Over" - Crowded House (who
doesn`t love this 80`s icon?? )
"Another Day" - Paul McCartney (just about
the perfect bassline--does it all! Have your cake and eat it too!)
"Under the Bridge", "Otherside" - Red Hot Chili Peppers (just because...)
"It`s My Life" - No Doubt (80`s Talk Talk cover still has one cool bassline.The bass is the star in this one)
"Stuck In the Middle (With You)" - Steelers Wheel (cool,retro-sounding song with sweet bassline)
I realise your band has to play what your audience/crowd likes and wants as well as the band playing music that defines them. Just one fledgeling bass player`s opinon(for what it`s worth).The proverbial $0.02 worth,I guess.
Good luck!
HosMan