Science does not allow us to be sure of what things are, but rather of what will happen: scientific knowledge, and "truth", is about consequences, implications, and relations more than it is about "what things really are".
The purpose of building theories is to try and describe patterns of cause and consequence, so that we may extrapolate them to domains where we have not yet explored and/or better understand how that what we get when we do explore those domains relates to what we have already explored. That is, so that we can ask a question of the form "what will be the consequence if I do X?" and be able to have a trustworthy answer even without necessarily actually going and doing X (which may not be feasible).
Hence while it's common to hear it, ideas that there are "true" and "false" theories aren't really correct: there's only better and worse theories in terms of being able to cover a larger domain and make fewer incorrect inferences regarding those consequences - but no theory can be assured of capturing everything for the totality of all empirical investigations is only ever going to be finite. It is entirely possible (though we have no a priori reason to assume) that, say, the model of things as "spacetime" actually fails if you could somehow manage to "get over the cosmic horizon" - or even just if we were to set out suitably long into space now. It is possible that subatomic particles may really be little gnomes. It's just that there isn't anything unambiguous to be gained in terms of extrapolating the patterns of consequences we see.
You can also think of it as a form of "data compression" that we perform using our intelligence: a theory compresses a large sum of empirical data - perhaps imperfectly - into a small, cogent set of generating rules. Indeed, this is how proper, dumb, data compression algorithms work: they try to find patterns they can use to shrink the size of a piece of input data. And just as with data compression, the more fidelity and more data they can get while still retaining a reasonable size output, the better. But the compression is not unique: different algorithms may produce very different compressed outputs, and likewise there may be a variety of very different theories that we can use for "compressing" what we have now.
Hence, if there's anything that science does say about "what things are", it's that they are, in fact, compressible as such with such good fidelity.
So back to the question - does "space" get "bent" by gravity or not? Well, space - or more properly space-time - is a human construct, an intellectual construct, or a social construct: it's something that we humans made up to try and compress our empirical data and it works pretty well and lets us extrapolate those consequential relations. In that regard, its behavior is fully defined by the theory we construct, so the answer to your question is yes, gravity bends - or better - is a bending of - spacetime, because that is part of what "spacetime" as we've defined it, and found makes it useful in this regard, is. And it's also the most widely-applicable such construct we have so far - but not necessarily the most convenient or most useful: in day-to-day work, the simpler Newtonian system is entirely adequate.