I can "see" why you would suggest that but to represent the past tense in English you just need a 'd', right? Besides, adding the eld to bing would be making it a completely other word (?).
Please, I am just thinking out loud, NOT making any judgements. Your idea is as good as any.
What about bing-d? I don't think it would catch on because folks are more inclined to to shorten words and the hyphen might be too laborious a task for them