For my baby, if I burp her after she’s fallen asleep, she will wake up and not be able to go back to sleep again (she’s the super alert kind of baby), but many babies are able to go back to sleep easily, so you can quickly burp her and put her to bed thereafter.
Burp her while she sleeping.. I did that for the night feed. I make sure he burp b4 I put him back to cot.