Saxophonists are almost always better trained than bass players. You already have a lot of what you need. The proof is in the responses here. Most of them are just guesses from bassists that don't or can't play what's shown in the video, as opposed to actual time-proven methods.
Ultimately, if you want to play in the style of what you hear in Bruno Mars tunes, transcribe the bass parts you hear in Bruno Mars tunes. Once you have that down, do the same with other material that informed the Bruno Mars stuff. It's that simple, and some of the advice here is so far off track that you may as well be asking the same question in a Dungeons and Dragons forum. Honestly speaking, rolling 12-sided dice may be less of a time waster than some of the stuff you've seen (and will see) here already.
In bass parts like this, there are stylistic devices and approaches that can only be absorbed by studying them and how they work over the existing harmony. No matter how many arpeggios, modes, scales, "saxophone songs", or other such studies you try to do, none will help you learn to play like that if you didn't do the transcription work. It has to be BASS transcription work, because learning Charlie Parker solos on bass will only get you fired. You have to immerse yourself in the music you want to emulate, and what has been recommended to you so far won't really help. Musical style and musical grammar are two different things, and ideas are more important than 1-3-5-7. You learn ideas from transcription and they, in turn, fuel your own. The flawed scale and arpeggio advice, no matter how well-intentioned, will continue, but transcription is the key to the lock.
Every bassist I know (myself included) that really does play in this style learned it from other players and copying from records. If you go to a club and see a guy playing like this, he'll say the same thing. He won't say he got it running scales and arpeggios.
Scales, modes, and arpeggios won't help you at all with rhythm, note choice, note length, and compositional techniques, which are as important as the notes themselves.
The Bruno Mars bass parts you hear are not groundbreaking material - it's sourced from Stevie Wonder and Parliament/Funkadelic synth bass parts, as well as Pino Palladino, Anthony Jackson, and James Jamerson electric bass parts. It's obvious the people that wrote those Bruno Mars bass parts loved and studied that music. Bruno Mars himself certainly did. None of it was created in a vacuum - there were influences. If you spend time listening to the music that this bassline material comes from and learning it verbatim, you will eventually figure out how those players did it themselves. There's no shortcut except to do that. Just copy the masters.