Are viruses self-propelled?
All of your reasoning is correct - viruses are not motile (i.e. not self-propelled). 

I don't understand why you think this would cause a difficulty in the case of bacteria.

Edit in response to comment @Remi.b

Some cursory research on estimating probabilities of collisions between particles engaged in random walks has revealed some very challenging maths. So I decided to simply look at some data.

Remarkably there is a fairly recent paper describing investigations of the kinetics of bacteriophage adsorption.


  Moldovan, et al. (2007) On Kinetics of Phage Adsorption. Biophysical Journal 93:303–315


I didn't realise it was still possible to publish papers like this, but in fact it is very interesting. For our current purposes we only need to consider the data presented in Figure 3, which show that when E. coli cells at a density of 108 cells ml-1 are mixed with bacteriophage &lambda; at a density of 5 x 104 particles ml-1, then 90% of the phage have attached to a bacterial cell within less than 10 min.

Just to relate this to a real life situation, it is estimated that sea water contains bacteria at a density of 106 cells ml-1 and phage at 5 x 107 particles ml-1.