Messagebird.
Not only can you bulk send marketing messages you can also pay for a long number or shortcode and receive replies and respond to them.
You will need to think about what you need it for and you will also need to make sure you have a robust policy in place that shows that everyone on your list has opted in to receive SMS messages, because opting in for Emails is not the same by regulation. But Messagebird will guide you on how to go about gaining opt-in permission.
Do not listen to everyone on this site who is talking about it being a waste of time and will be regarded as spam, they are talking absolute nonsense. As long as the people who have opted in are interested in what you sell/provide, and you are not spamming random strangers, then bounce rate is very low. Just limit it to around 1 message a week if possible, unless it is for notification purposes. If SMS was so bad, why do all businesses offer it, for example Dominoes Pizza, to great effect. SMS is not the issue, it is the messaging and how it is used that can be an issue.
On a side note to the posters on this thread. Giving the answer "Google it" is not good enough. The Forum (and Website) is about educating, informing and giving advice to people who need it. You should always presume that they have already "Googled it" and have struggled to find exactly what they need and have resorted to registering (which is a pain to do) to get a bit of advice or a recommendation that might help them to find what they need.
For many of you who responded (rather sarcastically, both on this post but on many others too) you give the impression that everyone must be an idiot, it devalues the importance of the forum and overall it kills it off as people browse it for information and all they see to every business question is lots of sarcastic "Google it!" answers. That doesn't add any value, but instead strips away a valuable resource that could help someone from making the same mistakes we have all made in becoming business owners.
If you have nothing positive, constructive and extremely valuable from your own experience to give, and can only offer a sarcastic reply, then step away from the Forum and vent a bit on Twitter. Other people who are here, trying really hard to make a life for themselves and their families by building up a business, do not gain anything from you having a bad day and wanting to throw some sarcastic shade their way. Give them a break, and if you cannot give 100% with your replies, just don't reply at all and leave it for someone else to help.
Sorry to rant but whenever I see someone annoyed at the lack of help from a community that has a forum to literally help people, and they talk about leaving the forum as it is toxic. it makes me frustrated and makes me wonder what YOUR Customer Service reputation must be like if you think you can help people by giving nitpicking and sarcastic replies.