Converting Multi-Select to a Text String

public static void setBUKey(List<Business_Metrics__c> newTrigger){
        
        String buKeyList;
        String buKey;
        
        Map<String,Business_Unit__c> buMap = Business_Unit__c.getAll();
        for(Business_Metrics__c bmx : newTrigger){
            buKey = NULL;
            if(bmx.Business_Unit__c != NULL){
                buKeyList = bmx.Business_Unit__c;
                List<String> buValues = buKeyList.split(';');

                for(string s : buValues){
                    system.debug('s: ' + s);
                    if(buKey == NULL){
                        buKey = buMap.get(s).Key__c;
                    }
                    else{
                        buKey = buKey + ', ' + buMap.get(s).Key__c;
                    }
                }
                bmx.Business_Unit_Key__c = buKey;
            }
        }
    }