How are the correct tRNAs transported to the ribosome?
The only way I can imagine this happening is that all types of tRNA+amino acid reach the ribosome, bombarding the ribosome, and the ribosome will 'accept' only the one that matches what it is waiting for.


Yup, basically.  This is an extremely cool figure showing the process. There are various elongation factors that aid the process, such as EF-Tu, which essentially waits until there is a good codon-anticodon match before hydrolyzing GTP and allowing the tRNA/amino acid to enter the ribosome.

This process can be particularly salient when you look at a concept such as codon-usage bias.  Certain tRNAs are more common in the cell, so if a given mRNA uses codons to match those tRNA instead of matching other degenerate but less common anti-codons, translation will occur faster.  This is more obvious in organisms such as E. coli where growth is paramount.