Competing in this category when there are so many dominant incumbents is really difficult. You'll need a product that significantly leapfrogs that of the existing leaders, which means it's likely mobile-first and focuses on a simplified, minimalistic user experience that delivers on the core use case of these apps.

To answer your question as you asked it:
1) Build the best product in the category;
2) Find a few key reference users (Social Media Managers at known companies who are themselves influencers about social media management) who are willing to declare your product as better than anything else;
3) Make it easy for enterprises to adopt this and establish some use cases that demonstrate how the more users who use this within a group or enterprise, the better their business results are vis a vis social media.
4) Buy inexpensive ads (Twitter is likely best) promoting these case studies encouraging sign-ups.
5) Talk to everyone who signs-up and hold their hands and lead them to become advocates for your service AND paying customers.

The challenge is that customer acquisition costs or even lead costs are high, driven up by the significant cash that the incumbents can afford to spend on acquiring new users & prospects.

Virality has proven difficult to achieve in this product category so it's really a function of convincing users to flee their existing tool in favor of an unknown, unproven product.

Happy to talk to you in detail in a call.

I think it is dangerous to look at it from a 'top 5 options to gain steam' point of view. Those are tactics that can help, but it is extremely important that you first define a strategy behind it.

To significantly increase your chances of success (and avoid extreme overwork trying 5 tactics at once, which often causes burnout), I highly suggest you do two things :
1 - select a specific industry
2 - select a specific geographic area

The best parallel I can do is with Starbucks. It looks today as if they are everywhere. But in reality, they started small, tested and tuned their 'system' locally, and gradually expanded geographically.

Facebook did the same (started by only focusing on the academic market, on one specific campus, with a clear focus on the 'dating' aspect, and then expanded).

A clear message is very important in terms of customer acquisition because a high level of specificity creates an 'this is for me' reaction, which instantaneously creates trust in your solution (one size fits all is dead).

Think big, but start small. We boot-strapped our company for nearly 4 years, and I wish I had received that advice earlier.

The idea there is find a few local businesses or friends to test out the product. Everything works in a vacuum, but you need real people before you can approach Kraft or CitiGroup.

Second is don't give it away. Show that someone is willing to pay for your idea.

You need to be sufficiently differentiated from the incumbents so you're the first-best solution for a group of potential customers (not 6th-best, which you will be if you try and compete head to head with the Hootsuites of the world).

As an example, Buffer came along several years after Hootsuite was founded. It was a simpler, faster way to post content to multiple social media channels. They focused on consumers or small businesses, where Hootsuite couldn't / wouldn't compete. By differentiating well, Buffer was playing a different game than HS, and gained significant traction.

In terms of how to differentiate, you may get lucky, but odds are you'll figure this out by talking to customers to learn what problems they have when managing their social media accounts (start locally and always ask for a referral to new people).

Happy to chat further on a call.

Being able to set yourself apart from the rest of the category is critical to your success. As a bootstrapped startup, niche targets will likely be an ideal choice since cash and resources are limited.

In addition to Tom's response. Connecting with influential blogs and those that have a following will help significantly in getting user traction based on their recommendations.

Creating videos and tutorials to solve problems or poitn out pain points that you product can address may be a low cost marketing effort.

Don't forget to test and analyze your signup data in understanding what is the trigger for your users to signup and look for ways to exploit it.

Depending on how robust your product is, you can look to establishing strategic partnerships to leverage other people's networks and or brands.

Hope this helps.