We report a H2 emission survey of five bipolar outflow sources (NGC 1333, M2-9, As 353, S106, V645 Cyg), and one region of shock interaction between an H II region and molecular cloud (NGC 281). Two of the sources (M2-9, NGC 1333) were detected in the v = 1-0S(1), and Q-branch transitions of H2, and we provide a detailed analysis and modelling for these cases. The probable mass of shocked H2 is shown to range between 1.4 10-6 and 4.2 10-8 M⊙ for M2-9, and ≈ 2.5-4 and 1.9-10 M⊙ in the case of NGC 1333, although the latter values may require increasing by a factor of a few when due allowance is made for extinction. A detailed analysis for the core of M2-9 indicates that the ionized zone is extremely compact, and our Brackett line measures support other evidence in suggesting a high core extinction, large emission measure E~4 1010 cm-6 pc, and a projected angular radius θc~0.04. Similarly, it is apparent from the H2S(1) line strength that the core expansion velocity must be low and less than ~ 1 km s-1 (a constraint which is also required on dynamical grounds). Finally, CO J = 3-2 observations of the source failed to detect emission above a 2σ limit of T*R ~ 0.4 K, and this is shown to imply a probable expansion timescale of ≲2 103 yr
