Like the other answer to this question says, I believe that the gifts the shepherd offers his love are meant to be hyperbolic representations of his love. In other words, one should not view the gifts mentioned in the poem as literal offerings, but as exaggerated examples of the idyllic and idealized nature of the shepherd's love. Take, for instance, the fifth stanza:

A belt of straw and Ivy buds, 
With Coral clasps and Amber studs: 
And if these pleasures may thee move, 
Come live with me, and be my love. (17-20)

In my opinion, many of the gifts the speaker offers his beloved are pretty ridiculous and are gifts that cannot possibly be given by a simple shepherd.

For example, the shepherd can surely not give his love a table made of ivory.  And no one can give food that would be as precious as what the gods eat.  The speaker is clearly being hyperbolic here -- they are things he can never give.

As for the other things, like a bed of roses, I suppose they would be possible.  Those other gifts sound pretty pleasant to me -- very restful.  To sit by a stream while birds sing, that sounds pretty restful and romantic.