Green’s Dictionary of Slang

(orig. RAF) to wander, to travel, constr. with a prep.; thus beetle in/up, to arrive; beetle off, to leave.

1918		Colonist (NZ) 21 June 7/4: To ’beetle’ signifies to ‘quirk about’ in an aeroplane [...] ‘To beetle round in a rumpty’ [...] means to flop about in the air in a certain type of old-hasioned almost fool-proof machine, offcially known as a Maurice-Farman, but popularly alluded to as a rumpty .
1919		W.H. Downing Digger Dialects 11: Beetle about, fly aimlessly (of an aeroplane).
1920		Marvel 8 May 11: Dat’s what you say [...] Beetle off.
1930		‘Leslie Charteris’ Enter the Saint 114: As soon as Whiskers has rumbled that joke, you, old haricot [...] will beetle in and arrest the lot of us.
1934		Wodehouse Right Ho, Jeeves 34: And with these heartless words she beetled off.
1953		A. Buckeridge Jennings’ Diary 136: He’s just beetled off on a top priority secret important mission.
1959		I. & P. Opie Lore and Lang. of Schoolchildren (1977) 212: Beetle off, bugger off, bunk.
1968		A. Buckeridge Jennings in Particular (1988) 23: Perhaps they’ve beetled off.
1978		(con. 1940s) J.G. Farrell Singapore Grip 114: Come on, I’ll show you around quickly and then we’ll beetle off.
1985		A. Payne ‘Minder on the Orient Express’ Minder [TV script] 24: Arthur beetles off to the caravan.
2000		Guardian G2 28 June 7: Another nun beetles up and whispers in her ear.