Should both business partners have access to bank account?

You sshould review the LLC's operating agreement provisions regarding authority for specific actions and access to books and records. Are you both managers as well as members? Although it may simplify matters if one has primary responsibility for writing checks, it's unusual to exclude one of two members from any access.

The general rule on this is that all partners (or in your case, LLC members) have equal access to company funds, assets and property, but in most states, you can allocate responsibility over financials and other authority in your operating agreement, as long as it does not conflict with your state's LLC statute. Look to your operating agreement first, and in the absence of a clear provision on the issue, look to your statute for the default, legal presumption. If neither answers your question with specificity, reach out to a local business/LLC attorney for precise guidance. Best wishes to you and your business.

Operating agreements may be amended and I recommend that you both sit down to evaluate the existing agreement (assuming there is one) to uncover any language regarding access to the banking accounts. A business attorney can assist on this and can also -re-write an agreement to be more comprehensive regarding your partner duties. Theoretically I agree that as a fully vested, equal liability partner, you should have access to the bank accounts if for no other reason than sound leadership of the company.

It depends on what your operating agreement says. This would be addressed in there. A full consultation would be necessary to properly advise you.

Your answer is in your Operating Agreement, but there is no reason that both Members should not have equal access. One could easily argue that fiduciary duty compels them to have equal access.