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When playing so-called "walking bass" lines with bands playing 1920's-1930's music, don't actually "walk" very often.
Going up or down the scale (if the goal is to help the band sound like an actual band - rather than a "jam session"...ie. "a cluster of musicians which 'jam' pitches together, which don't always line up") should be limited to only when doing so lines up with passing chords and (well...) when the pianist/banjo/guitar player(s) are actually respecting the implied or originally-composed passing chords.
Otherwise (if playing a 4-to-the-bar bass line on a particular chorus or entire song), it may be better to repeat a pitch on 2 or 4, or to arpeggiate (and with the arpeggiation neither being over-the-top, nor some monotonous/distracting 1-5-1-5 thing, and nor clashing with commonly used "front-line" players' harmonies.
You'll need to use your ears and your musical taste...If neither are particularly developed in this group of styles, develop them.
one other tip:
LEARN the songs that you plan on playing. In the past, I've posted about "learning" being the highest version of understanding of music...above BOTH "memorization" and "reading". KNOWING songs (rather than only memorizing, re-reading, or reading on-the-fly) allows for much more thoughtful and wiser anticipation (thus much better decision-making, regarding bass line note choices).
bloke "again...IF actually striving towards sounding like a band which - whether it actually does or does not - rehearses"