Synonyms for Bum around:

n.

go, travel, DO, see the world, roam, island hop, come, explore, get around. rest, wind down, idle away, recharge your batteries, while away, sit back, bask, laze, relax. bum around (noun)
bum about, Arse About, lounge around, loll around, fuck off, frig around, Arse Around, waste one's time, lounge about, loll, loaf.

v.

bat around (verb)
roam.
dawdle (verb)
loll, laze, loaf.
loaf (verb)
lounge around, relax.
roam (verb)
travel.

Other synonyms:

island hop, roam. explore. get around, travel. come. arse around
Arse Around.
Other relevant words:
laze, roam.