Both are correct. If you say 'dus ik blijf thuis', you use 'dus' as a coordinating conjunction, connecting two main clauses. After a coordinating conjunction (there are only 5: maar, en, of, want and dus) nothing changes in the word order. If you say 'dus blijf ik thuis', you use 'dus' as an adverb. Because this adverb comes before the verb 'blijf', inversion occurs. Both possibilities are equally correct and there isn't a difference in meaning. This only goes for 'dus', not for the other 4 coordinating conjunctions.