Recent efforts to improve the efficiency of neuromorphic and machine learning systems have centred on developing of specialised hardware for neural networks. These systems typically feature architectures that go beyond the von Neumann model employed in general-purpose hardware such as GPUs, offering potential efficiency and performance gains. However, neural networks developed for specialised hardware must consider its specific characteristics. This requires novel training algorithms and accurate hardware models, since they cannot be abstracted as a general-purpose computing platform. In this work, we present a bottom-up approach to training neural networks for hardware-based spiking neurons and synapses, built using ferroelectric capacitors (FeCAPs) and resistive random-access memories (RRAMs), respectively. Unlike the common approach of designing hardware to fit abstract neuron or synapse models, we start with compact models of the physical device to model the computational primitives. Based on these models, we have developed a training algorithm (BRUNO) that can reliably train the networks, even when applying hardware limitations, such as stochasticity or low bit precision. We analyse and compare BRUNO with Backpropagation Through Time. We test it on different spatio-temporal datasets. First on a music prediction dataset, where a network composed of ferroelectric leaky integrate-and-fire (FeLIF) neurons is used to predict at each time step the next musical note that should be played. The second dataset consists on the classification of the Braille letters using a network composed of quantised RRAM synapses and FeLIF neurons. The performance of this network is then compared with that of networks composed of LIF neurons. Experimental results show the potential advantages of using BRUNO by reducing the time and memory required to detect spatio-temporal patterns with quantised synapses.