Patients receive bevacizumab IV over 30-90 minutes on days 1 and 15 and oral erlotinib hydrochloride once daily on days 1-28. Treatment repeats every 28 days in the absence of disease progression or unacceptable toxicity. Patients undergo laboratory studies to determine epidermal growth factor receptor (EGFR) and phosphorylated-EGFR protein levels using initial diagnostic biopsy specimens by immunohistochemistry (IHC) for correlation with clinical outcome. Levels of proteins through which EGFR signals, including Akt, phosphorylated-Akt, mitogen-activated protein kinase (MAPK), and phosphorylated-MAPK, are also determined using initial diagnostic biopsy specimens by IHC and correlated with clinical outcome. Total and free serum vascular endothelial growth factor levels are determined at the start of study and prior to course 3 by enzyme-linked immunosorbent assays (ELISA).