We are a bundle of processes, and every moment are remaking ourselves, using the materials inherited from our past.
According to Mahayana this is more or less right, but only as a simplification. If you dig in-depth, you eventually reach the limits of description and hit Emptiness, as Nagarjuna loved to point out.
Buddha said that almost all
dharmas (things, phenomena) are
saṅkhāras (bundles, assemblies). Dharmas that are not sankharas include Nibbana, and, according to some schools, but not all, Akasa (sky or space) and stuff like that (e.g. Time). Buddha explained that
saṅkhāra-dharmas emerge when causes and conditions "come together" (
samudaya) in a certain configuration and disappear when one or more of the necessary causes or conditions goes out. This is the fundamental principle behind the key teachings like Anicca (impermanence), Anatta (as explained through inability to control anything), and therefore Dukkha (esp. because of unreliability). It is also the fundamental principle behind Second and Third Noble Truths, explaining that Dukkha is also a sankhara, emerging when certain causes come together, and therefore can be stopped and prevented (
nirodha) by removing one of the necessary causes, namely Craving (
tanha) for things to be different than they are. It is also the fundamental principle behind Buddha's liberation from death, which, too, considered a sankhara and is traced back to its causes, among which Buddha identifies birth as the key element we can use to stop/prevent death, and then on the next cycle, taking birth as sankhara and looking for its causes, Buddha finds identification and appropriation (
upadana). Note that Buddha never said death has no other causes other than birth, it obviously does (such as a strike of knife) - but birth is the key element we can work with - and so on all the way to Ignorance. So as you can see, the bundle theory is at the very center of Buddha's teaching on Three Marks of Existence, Four Noble Truths, and Twelve Chain of D.O. - the core of the core of Dharma.
Now, if we expand this analysis to include Mahayana perspective, we could note the following:
When we say "We are the bundle of processes", what exactly does that mean? First of all, what is a "process"? My teacher explained that processes can be seen like chains of events, like a sequence of billiard balls pushing each other. This can be understood. The billiard balls keep pushing other balls until they all get in a certain configuration temporarily and this configuration is a person (or other dharma). However, are we saying that each dharma (e.g. a person) is literally a bundle (sankhara) of a specific number of precisely identifiable processes? How many processes are there then? Where are the boundaries of each process? Is it the same number of processes over one's lifetime or does it vary with time? As soon as we start asking these questions we must necessarily realize that these "processes" we are talking about, are themselves not concrete. They are just a manner of speech. The processes are approximate abstractions, conceptual simplifications for describing the infinitely forking and joining network of causes and conditions leading to emergence of phenomena.
In Mahayana, we say that all Dharmas are empty. We also say that so called "Hinayana" (which is not necessarily a name for Theravada, just a name for simplistic/superficial understanding of Buddha-Dharma, because indeed there are Theravada practitioners who clearly understand this stuff), we also say that so called "Hinayana"-level of understanding naively assumes that dharmas that e.g. people are made from are themselves concrete and real, that they exist in the ultimate sense. No, according to Mahayana, they are not. According to Mahayana all this talk about processes and dharmas is a useful simplification. Everything is a simplification. Once we go all the way, we reach the limits of description and see that final reality is unspeakable. We call this Emptiness.
So, to say "we are a bundle of processes" is more or less right as long as we understand the limits of the semantic context within which we are making this statement.
...and every moment are remaking ourselves, using the materials inherited from our past.
What is "every moment"? Is there such thing as a single moment? From the above it should be clear that the answer is No. The dimension of time is infinitely slicable into infinitely smaller pieces. There is nothing like single moment, because the duration of moment depends on the scale of observation, which depends on perspective.
Are we really remaking ourselves? Or are we maybe "being remade"? Who is the driving force here and are we really in control? According to Buddha, it is a combination of the forces of inertia (latent results of past action or karma) plus the force of choice and determination being made in the now. So we can't say that each of us literally remakes oneself in isolation from everything else. We are being made by our past and we make ourselves and each other with our choices.
Using the materials inherited from our past.
This sounds like "material" is something real and tangible that actually stays around, with things being made from combination of materials. This is not a Buddhist position, this is simple materialism. In Buddhist understanding, once you look close enough you see that so-called "material" is actually made of sankharas each of which is a just a focal point of interaction of other sankharas and so on. There is nothing tangible here, just interactions upon interactions. These interactions do not actually stay in the same place, they keep interacting, which is why things morph all the time, things get old, drift apart, and new things grow from them.
In Zen tradition this is well-explained by Dogen in his very important work "Time-Being".
So it's not like something tangible actually gets "inherited from the past". It's more like spreading and intersection of multiple waves - each next moment is a development - or unfolding - of the previous moment according to the rules of interaction. What's inherited from the past is form as well as force, the form of force, combination of energy and information.
Finally, see how it's saying "we are" and "our past"? That's identification and appropriation right there! Why is this stuff "we" and what makes that past "ours"?
Now, with all of the above, when you say "we are a bundle of processes, and every moment are remaking ourselves, using the materials inherited from our past" - and while saying this you understand what Buddhism would mean by "bundle", "process", "moment", "remaking", "materials" and "inherited from the past" - as well as the limit of what's meant by "we" and "our" - then you can understand the picture that this phrase is trying to paint.