If you already have a 2, 5 or 10 year visit visa for the UK (e.g. for business or tourist purposes), you can study on this visa for up to 30 days in a 6 month period and therefore do not need to apply for a Tier 4 (General) part-time visa. Your reason for holding the business or general visa must still be valid, and you may be asked for evidence of this when entering the UK. This may be evidence of required business trips to the UK, or a personal connection to the UK that requires you to visit on a regular basis.
If you do not already have a long-term visit visa, but make frequent business trips to the UK, it may be worthwhile enquiring if your company can support your application for a long-term visit visa. This would allow you to both study at LBS for up to 30 days in a 6 month period, as well as continuing to carry out your business activities, within the limits of activities permitted on a visitor visa.
You are not permitted to bring dependents. Your dependents will need to apply to come to the UK in their own right as general visitors. They will not be able to work or study.
It is not possible to concurrently hold more than one visa for the UK, so please be advised that applying for a Tier 4 (General) part-time visa when you already have a business or general visit visa may result in the latter being cancelled.