Experimental studies of neuronal cultures have revealed a wide variety of spiking network activity ranging from sparse, asynchronous firing to distinct, network-wide synchronous bursting. However, the functional mechanisms driving these observed firing patterns are not well understood. In this work, we develop an in silico network of cortical neurons based on known features of similar in vitro networks. The activity from these simulations is found to closely mimic experimental data. Furthermore, the strength or degree of network bursting is found to depend on a few parameters: the density of the culture, the type of synaptic connections, and the ratio of excitatory to inhibitory connections. Network bursting gradually becomes more prominent as either the density, the fraction of long range connections, or the fraction of excitatory neurons is increased. Interestingly, biologically prevalent values of parameters result in networks that are at the transition between strong bursting and sparse firing. Using principal components analysis, we show that a large fraction of the variance in firing rates is captured by the first component for bursting networks. These results have implications for understanding how information is encoded at the population level as well as for why certain network parameters are ubiquitous in cortical tissue.