The difference is actually not between bidding and biding, it is between bid and bide. The latter means to dwell on something, and hence its usage in the phrase: bide one’s time.
Bide is actually an archaic term now and is not used commonly other than in the phrase given above.
Tool tip to remember the difference :
Just Remember: Bidding comes from ‘bid’ and biding comes from ‘bide’ .
Examples of incorrect uses of bidding and biding:
1. People were amazed to see how a low cost won the biding.
2. He is very honest and law bidding.
Examples of correct uses of bidding and biding:
1. I went their because of her bidding.
2. He was biding his time in the hope for a change.
A Quick Recap:
Bidding means to offer to pay a particular amount of money for something that is being sold: “He plans to stop bidding on his house by making a counter offer.”
Biding means waiting for the right time before doing something: “He is biding his time so that he can enter the bidding process at the right time and stop bidding on his house by making a counter offer.”
The confusion regarding the ING form Bid and Bide can be remembered from General ING Spelling Rule
When a verb ends with a consonant-vowel-consonant, and we put STRESS on this sound in speech, we double the last consonant and Then we add ing.
run => runn + ing => running
stop => stopp + ing => stopping
Bid => bid+ ing => bidding
When a verb ends with the letter e, we first remove it, and then add ing.
take => tak + ing => taking
make => mak + ing => making
bide => bid+ ing => biding