Sorry, I can't imagine why substituting a b sound for a p would be intentional... it just sounds odd. I've never heard anyone say it like that.
It kinda-sorta-maybe makes sense as a way to show fatigue post-workout, but that'd be better served by a more tired/breathy pronunciation (like a drawn-out 'biiiih-chen', maybe even with an inhale inbetween). Even more complicated is the energized attitude and that if you work-out first he won't say it until after eating (allowing him to Popeye). So it really seems like a higher-energy (contrasting his normal laid-back attitude) and faster pronunciation (maybe even b'ch'n') would be more in-tune with how he acts.
Also Re:English Bernard, does your English Laverne voice actor have English as a second language? She has more of a foreign accent (one I can't really recognize) and less of a crazy voice. Sort of makes me think maybe Laverne is an exchange student (maybe she was kicked out of medical school in her home country for doing something... unethical... or because she had a breakdown/episode? Either one barring her from medical practice, but not in the US?) so it doesn't feel too out-of-place.