All the parts you described fit a Centurion Accordo from 1988

The Centurion Time Machine was exclusively distributed by
WSI NEWBURY PACK CA91320

_vintage-centurion.com/models/sports-rec/accordo.shtml

I have a green and white Time Machine from 1988 but it did not come with the Time Trial/Triathlon clip-on bars

_vintage-centurion.com/literature/catalogs/1987_Centurion_Catalog.pdf
_vintage-centurion.com/literature/catalogs/