I would bootstrap as long as possible.

As long as you're able to engage engineering resources for continual product enhancement; the customer support team to ensure customers are churn-proof happy; the marketing team to generate awareness, leads, and optimize the sales process; and the sales team to close business, keep going on your path.

Where things get tricky is in terms of competition. If you're bootstrapped, it's harder to compete against a well-funded adversary (or adversaries) because they can do much more in terms of generating awareness. Their marketing team can attend many conferences. If your sales cycle is aided by in-person contact, conference and trade shows could be important. They are not cheap.

Your marketing needs may also require a huge amount of demand generation. This can become really costly. (See the Fan Duel sports betting marketing campaign in Q3/4 2015. Mega expensive!).

Depending on your product category, investment can also play a role in how prospective customers perceive you. If you're selling to the enterprise, having Blue Chip backing from Kleiner Perkins or Sequoia will impress those who look for this external validation. (You've surely heard of the “No one ever got fired for buying IBM” statement?). VC funding also helps with publicity, and media coverage if you care about that and need TechCrunch clips.

There are many successful startups that never took any money. The vast majority or startups, in fact, don't.

Based on your description above, though, it doesn't seem as if my thoughts apply to you. If you already have partnerships that are working for you, global customers you can leverage in those regions, a product that is clearly providing value to your customers, and you can fund growth from cash flow or other options (debt financing, perhaps), I'd keep to your path. The larger and more successful you become, the better the terms you can negotiate if and when you decide you can't live without outside investment.