If they exist, they will be at Lincolnshire Archives.
To find out what records the Archives hold for a particular parish start here.
http://tinyurl.com/5vmkarlFor Market Rasen, click on the M-0 section, then the downloads tab.
Market Rasen is
not in alpha order on the list.
The parish registers are under PAR1. Your dates are covered by PAR/1/5 (though in actual fact the registers will have been filmed so you'll look at the fiche which have different reference numbers.

Bastardy bonds will be part of the Overseer of the Poor section so you want PAR13 (see list on first link I gave).
Within the umbrella of 'Overseer of the Poor' you then have various documents, broken down into subsections with the dates.