Are there any robust methods available to predict the spread of invasive species if it is done for a smaller geographical area (ex. a biosphere reserve or national park etc).
First, MaxEnt is a presence-background model not presence-absence, and also BIOCLIM is a presence-only model. The presence-absence models are a different group of modeling approaches such as CART, MARS, SVM, GAM, GLM, etc.
Second, I suggest you trying OpenModeler Desktop which the last version I think is 1.1.0, in this platform you could find more than 10 modeling approaches for your study.
For invasive species only-presence models are recommended (see Jiménez-Valverde et al. 2011, Biological Invasions 13). Bioclim (or multidimensional envelope) and mahalanobis distances are suitable for invasive species (e.g. Aragón et al 2010, J. Appl. Ecol. 47).
If you want interpreting the observations (occurrence/abundance) as a result of several hierarchical processes including ecological processes and observation processes (detectability) you could use a hierarchical Bayesian species distribution models, like hSDM (R package):