Ask the author of a paper for suggestions of where to publish replication results I based my thesis on a published paper and ask its original author if he was interested in seeing the results. After approaching him (with your help provided: How to address an author showing replicated results from his paper? ) he replied


  Your application of the XXX method looks very good.  Congratulations,
  and thank you for sharing your work.


and made some recommendations about the bibliography. 

Now, should I end this conversation with a thank you or can I insist a little bit more and ask him if he thinks it can be published somewhere or even if he can suggest where could I publish.
(It's a bachelor thesis so it's not something groundbreaking, it's more of a replication paper).
Scientific method is based on the idea of reproducibility. So being able to replicate experimental findings, or not replicate them, is an important contribution to your community. Of course it would be more groundbreaking if you were NOT able to replicate results, as that would be a sign that there is more to learn. But even a mere replication using independent data would be make a solid paper. And of course, it matters all the most if the original paper found something really exciting. 

It is a bit different for "theoretical" papers as putting forward ideas when somebody else did it already, does not add much to the community understanding. Unless you derived the same conclusions starting from very different assumptions, or following a very different path, replicating theoretical ideas typically does not warrant a publication.

As for what journal, again it depends on whether you are using independent data/though process, and how relevant was your original result. You could aim for the same journal of the original paper, and if that fails, aim for something just slightly lower in ranking, and more field-specific. Good luck!