> The current theory is that particles are waves, or rather localized excitations ('bumps') in a field.

It might be more useful to think of it the other way around.

If you start with a quantum field which has an expectation value at every point in spacetime -- the electromagnetic field at its lowest energy, for instance -- then every departure from that fixed background is a perturbation of the field. The "quantum" part means that any perturbation takes on discrete values.

For example, perturbations of the electromagnetic field have discrete intrinsic frequencies and for any given frequency f they appear as 1 hf, 2 hf, 3 hf, 4 hf, ... but never 0.5 hf.

Those electromagnetic field perturbations (or excitations if you prefer, or in the case of our electromagnetic field, photons) localize when they interact -- the interaction is an all-or-nothing process and happens at a definite point in the universe, and the interaction produces a complete photon or consumes a complete photon.

We have promoted a wide range of classical field theories to quantum field theories by treating waves in the classical field as perturbations of the classical field's ground state, and we then quantize those perturbations. For example, a classical coherent electromagnetic wave with frequency f can be represented as a number of photons each with energy hf. Multifrequency electromagnetic waves just add more photons with different energies hf' or hf'', for example. Each photon's frequency hf, hf', hf'', and so forth determines the strength of the electromagnetic interaction that is carried.

In Quantum Electrodynamics or the Standard Model, when the frequency of a photon is extremely high pairs of non-photons can be produced (e.g. an electron and a positron). These pairs can go their separate ways, or mutually annihilate into a high-frequency photon. As the local energy-density increases we get more and more high energy photons, electron/positron pairs, and possibly other types of particles, all potentially existing locally for brief periods. To sort this out we use a mathematical procedure called perturbative renormalization, which essentially lets us declare some of these possible high energy interactions to be "marginal" or "irrelevant" to the physical system under study. This works very well in predicting experimental results up to very high energies.

General Relativity (GR) is a classical field theory. For decades relativists have worked with perturbatively renormalized gravity, which fixes a metric on a static spacetime background, and treats any perturbations of that metric (e.g. by the movement of a gravitational wave through the spacetime) much the same as we do with electromagnetism: a classical gravitational wave can be represented as a number of gravitons each with its own intrinsic frequency that determines the strength of the gravitational interaction it carries. Gravitons participate in all-or-nothing interactions that localize them.

There's a crucial point here though. Photons are a boson with spin 1, so they do not attract or repel or really interact at all with one another directly; they also do not electromagnetically attract electrons or positrons or other matter that feels the electromagnetic interaction; photons themselves have no electromagnetic charge. Gravitons are a boson with spin 2, so they attract like charge and repel unlike charge; they also carry a gravitational charge themselves. The whole particle zoo of the Standard Model has like gravitational charge, and so would only interact with one of the two possible charges of graviton in perturbatively quantized gravity; the other charge of graviton would be pushed away to infinity by the field content of the Standard Model (and also by the gravitons produced when the perturbations of the fields of the Standard Model propagate through the universe, and also by the gravitons produced when gravitons propagate through the universe).

Consequently at very high gravitational energies, we have to do more and more renormalization to deal with the production of gravitons as daughter products in a process similar to pair production at very high electromagnetic energies. Unfortunately, perturbative renormalization eventually breaks down as a procedure, and so we cannot declare possible interactions as "marginal" or "irrelevant". Moreover, we haven't yet discovered a non-perturbative renormalization procedure that would let us keep calculations of gravitational interactions at high energies tractable.

However, perturbative renormalizaiton works very well even some way inside the horizons of massive black holes; the breakdown happens close to the (classical) singularity. It also works very well when looking into the distant past of the universe, however in the extremely hot dense phase of the universe it also breaks down due to perturbative non-renormalizability. Thus at low energies, below the energy at which renormalization breaks down, perturbatively quantized gravity is a perfectly good effective field theory of Einsteinian gravity.

Detecting a single graviton is not plausible at our level of technology, but the detection or non-detection would say very little about the utility of the theory. The Higgs interaction described by a quantum field was useful (in that it corresponded well with experiments) for half a century before the Higgs boson (which has spin 0) was detected.

General Relativity does not restrict us to quantizing perturbations of the metric, however. There are other quantizations of the mathematical objects in General Relativity which are significantly different than the approach outlined above, and have their own advantages and drawbacks.