I second those saying that the lease is invalid. Transaction is pending the completion of the security deposit – which did not occur in a timely manner.
Did you run a credit check on these people? I would just move on to the next potential tenant. Bouncing on the first transaction is not a good idea, shows a potentially poor tenant – who you will have to be continually chasing down for rent. If this is in California – avoid this person. They can play the declare bankruptcy/non-appearance game to make eviction for non-payment nearly impossible.
Not safe to give bank account number (add routing number and guess at most recent check number – and forge away your account). Besides, if they already had the cash – the security deposit would not have bounced. That means that mentioning ‘direct deposit’ is a red herring.