The best examples that come to mind are when ordering food. As examples:
• You speak English and Spanish and are ordering a burrito
• You speak Thai and English and are ordering Tom Yum
I imagine it could depend on numerous things:
• You primary language or ethnicity
• What sort of restaurant
• Who you’re dining with
• Who you’re ordering from
• and probably a lot more…
I’m not very bilingual but I grew up with English and have spent a few months in Latin America.
I noticed that in English I now say Mexico the Spanish way when I’m with local people, but the English way when I’m visiting friends in the US. I always say it the Spanish way in Spanish, and don’t think I use any regional accents.