Hey @Gnockylefty – Welcome!
So, the answer to your question is one you’ve probably already guessed – practice.
I have been singing for years, and singing along to a guitar I was playing for a good long while as well. Bass is different, and I find even as seasoned as I was at the other two things, singing with bass takes a slightly different discipline. The key is being able to do one thing without thinking about it. Most of the time, you will be thinking about singing as your hands play bass “on their own”, but it does sometimes change.
One of the first songs I learned to sing and play bass to was “Jet” by Paul McCartney. It’s not a hard bassline by any stretch (for the most part, you’re keeping time on A on the E string – 5th fret). There are tabs on Youtube and elsewhere, but if you have trouble finding one, let me know and I can show you the version I practiced.
You mentioned Sting, but I’ll caution that he’s trickier than a lot of people give him credit for when it comes to singing with his basslines. You can find “Roxanne” here in the 50 Songs that came with the B2B coursework, which is a pretty good one. One of the first ones I did, when I was ready for a bit more challenge, was “Fragile”. It’s the opposite of what most people would think to be hard for singing while playing bass – very slow tempo, only one or two notes that go down the fretboard in a pretty simple pattern… BUT, its those long pauses and the syncopation that will really force your brain to pay attention. I love it for that.
Another Sting song that’s on the easier end to play and sing along with is “Wrapped Around Your Finger”. It’s again, a bit tricky, but simple enough to get the hang of after a few practices. I really like to do this one when I want to get serious about my singing and try to forget I’m playing the bass. Same with Carly Simon’s “You’re So Vain”. Both are good songs to try out if you’re used to your voice being the thing that carries the tune more than the guitar.