Yes, that's possible. Edit your plans then under the Workflows tab find the "Dynamic Conditions on other plans and CB Fields to show this plan and to allow subscribing to it" section. Here you can configure conditions for the plan selection during registration. In your case you'd edit the 3 plans you don't want visible to Business type and add conditions to check for that. Example as follows.

Conditions on CB Fields to show plan at registration
And following CB Field: PROFILE_TYPE_FIELD_HERE
Condition: <> (Is different from)
Value: BUSINESS_OPTION_VALUE_HERE

If you need this to apply to upgrades as well then be sure to configure the same under "Static Conditions on already existing subscriptions and CB Fields and Dates to allow upgrades" section. Example as follows.

Dates / CB Fields Comparisons
Date A, Field A or Value A: Following CB field
CB Field A: PROFILE_TYPE_FIELD_HERE
Date B, Field B or Value B: Constant Value or String (CB substitutions can be used)
Value B: BUSINESS_OPTION_VALUE_HERE
Condition 1 (> for Dates): A <> B (Value A is different from Value B )

Now those 3 plans should only be available to Personal accounts.

There's no way to run a $0 payment through payment processing. We bypass payment processing entirely for free subscriptions. Recommend just using email confirmation and maybe also moderator approval for free users as you can bypass both within your plans under the Workflows tab for paid users.