Sabernar: I live on NE 20th & Stanton (between Fremont & Knott) and bike past Wilshire Park every day. I also go downtown frequently, so I know the streets pretty well. There isn't a perfect route from Wilshire Park to downtown, but this is what I usually take:
ye olde google maps
Since you're heading to the Broadway Bridge anyway, I usually find it's fastest to just get to Broadway, and then zip down. You can make it from 21st to the bridge pretty quickly if you push it, but there's a lot of drivers on Broadway who pull stupid stunts, so I would advise not being in a hurry--about three out of five trips I get cut off by some jackass who crosses the bike lane without signalling.
The only alteration from the linked route I would suggest is zigging down to 20th or 19th after you get down the hill; 21st is fine, but anything just off that is going to be quieter, if a touch slower.