Yes, the movement in the bad debt account (the provision account) is an expense account. For example, if a company wishes to make a provision of $1000 for bad debts, it will debit the bad debt expense account and credit the bad debt provision.
If in the following year, the bad debt provision required increases to $2000, then the bad debt expense will be debited with $1000 and the bad debt provision will be credited with $1000, making the total provision $2000 ($1,000 in each year).