Bichel continued his outstanding domestic season to steer Queensland to a 199 in their first innings on a grassy pitch on Thursday.
He then backed that up with the ball (1-21), claiming South Australian skipper Darren Lehmann for 15. Fast bowler Joe Dawes finished with 3-26 from 13 overs.
Opener Greg Blewett was the only batsman to show resolve and was 34 not out in his team's 68 for five at stumps.
Victoria's Brad Hodge scored another century to dominate Tasmania on day one of their match at the Melbourne Cricket Ground (MCG) to bolster his chances of a national call-up for next month's Test series in New Zealand.
Hodge's 140 not out in a massive 388 for four put his side in a commanding position in the first of three matches Victoria must win to have any chance of reaching the final.
Apart from Hodge, Matthew Elliott scored 89 and Jason Arnberger 60 while captain Cameron White was 50 not out at the close.
Brisbane (day one): Queensland 199 (C Perren 58, A Bichel 47 not out, L Steves 46; S Tait 4-61, P Rofe 3-44) v South Australia 68 for 5 (G Blewett 34 not out; J Dawes 3-26).
Melbourne (day one): Victoria 388 for 4 (B Hodge 140 not out, M Elliott 89, J Arnberger 60; A Griffith 2-84) v Tasmania.