I often take the expo bike path to Culver City. It should get better this year when they finally connect the bike path to Motor, but until they do I usually take one of two routes:
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Take the expo bike path east until it ends at Overland, then take Northvale (a small residential street, but very hilly) Right on Motor (painted bike lanes but wide and feels fairly safe), Left on National (painted bike lanes, very low traffic), and when crossing Palms the expo bike path resumes again (you can get into the left hand turn lane on National but instead of completing it under the 10 just make a right onto the sidewalk to get back onto the bike path). You can take that all the way to Ivy station, or if you want to go further west I usually exit it at Durango, enter the parking lot there and cross Venice with the light onto Culver blvd which after 1 block has great bike lanes. You may be tempted to take Bagley but I recommend avoiding it, it's one of the few crossings under the 10, so many cars are aggressive.
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When I want to avoid the hills on Northvale, I exit the expo bike path onto Midvale, Right on Coventry, Left on Sprout, Right on Kelton (all of these are small residential streets). Then I take that all the way down to Venice. There's a protected crosswalk on Kelton to cross National, a light on Palms. If you cut back over to Midvale via Charnock there's a light on Venice. I've done this route very often and never encountered aggressive drivers on Kelton like I have taking other routes. You can also continue south on Midvale to Girard to Elenda which has a fantastic bike path -- stop by cofax for a good coffee.
Here is more information on the project to connect the bike path: https://ladotlivablestreets.org/projects/Exposition-Bike-Path-Northvale-Segment