your diocese has a prescribed process in place, first better find out what your diocesan particular law has set down, then within that framework work out the details. Where, when and by whom is it counted, where is it kept before counting and before depositing, where, when and by whom deposited, who prepares and checks deposit ticket.
Business mgr and/or bookkeeper should not be the same person doing the counting, they should verify the deposit tickets and bank statements, but this is bad practice open to abuse, because if their is a discrepancy they have no way to defend themselves from accusations. The person who enters the data on collection from the envelopes and list of checks should also be a different person, and the computer or hand system periodically checked and audited by the business manager. Our diocese has a computerized system, automatically sent to the diocese for audit.
When money is transferred from storage to counting area, it should be at least two people for security, same as trip to the bank.
There should be team of counters, all trained by bookkeeper or business manager in how to do it, how do endorse checks, how to run totals, how to allocate special collections etc. The same people should not do the same job every week or every time, so that when discrepancies arise they are easily noticed: if loose cash is usually around $500 and that suddenly changes when one team counts, that is a red flag for instance.
Former parish had four teams, so you counted once a month, everybody was cross-trained so whoever showed up knew how to do each part of it. If someone can’t handle part of the job, counting change (an electric gadget that counts change and drops it in the sleeves is worth the investment), note loose check info etc. simply cannot serve in this ministry. Run tapes for all totals and keep until the collection is deposited and verified or for as long as diocesan guidelines dictate, same with envelopes. Pastor should verify deposit ticket before it goes to the bank.