I am using phplist for this purpose and all your requirement can be fulfill using your own host .
well I recommend you to select a centos 64 bit os on digital ocean , then install phplist on it . this way you can send unlimited mails to your list . also bounce back can be handle on server for cleaning of invalid subscriber.I can configure all this for in this bid price .
About Me
hello, raza here, I am system and network administrator with more than 8 year experience .I can help you regarding this as i am available right now for any commitment and assure you that you will be not disappointed by me in any way. I have great expertise with Linux and Windows based services. I look forward to hear from you soon.
Regards