How to copy taxonomy terms of a node into a textfield using rules?
Well that was easy then.

Create a rule with this configuration.


Trigger the rule "After updating existing content" and "After saving new content".
IMPORTANT. Create a condition with "Entity is of bundle" and choose the desired Content Type. If you don't do this, not all the fields of the content type are exposed to rules for manipulation.
The Action is "Set Data Value" and as Data choose you text field (node:field-keywords in my case). For value choose your desired terms field ([node:field-business-categories] in my case).


Run a "Published" procedure on all desired nodes with VBO and you are done.

And here is the exported rule.

{ "rules_keyword_field_generation" : {
"LABEL" : "Keyword Field Generation",
"PLUGIN" : "reaction rule",
"OWNER" : "rules",
"REQUIRES" : [ "rules" ],
"ON" : { "node_update" : [], "node_insert" : [] },
"IF" : [
  { "entity_is_of_bundle" : {
      "entity" : [ "node" ],
      "type" : "node",
      "bundle" : { "value" : { "business" : "business" } }
    }
  }
],
"DO" : [
  { "data_set" : {
      "data" : [ "node:field-keywords" ],
      "value" : "[node:field-business-categories]"
    }
  }
]


}
}