I have been thinking about doing a piano recital on my party in July and planned on doing Bach harpsichord concerto no.1, but there aren't any recordings of the orchestra only. Do any of you know how I could find those kinds of recordings with the orchestra playing only so I could play along.?
There used to be a series of records called Music Minus One which released many concerto recordings with only the orchestra. Perhaps a search on "Music Minus One" may help. They are still around: http://digital.musicminusone.com/
The other possibility is to find a stereo recording where the soloist has been fed to both channels equally. The channels can be electronically subtracted (in the old days by hooking up speakers hot left to hot right with the grounds connected) but one may be able to a DAW to do this electronically. The orchestra will be out of phase with itself (like a big echo) but still able to be used for practice.
It seems that MM1 has BWV 1052 http://digital.musicminusone.com/j-s-bach-concerto-in-d-minor-bwv1052-digitally-remastered-2-cd-set.html
You could try a MIDI rendition, there are quite good ones out there, just do a google search. With a MIDI player that allows you instrument selection of muting (VanBasco Karaoke Player is good one and very simple to use), you can mute the harpsichord and play on top.
Now, soundwise a MIDI rendition will only be as good as the sounds you have available. The default windows General Midi sounds will surely not fulfil your expectations about the sound of a Baroque orchesta, not by a long shot. Perhaps you have a friend with a DAW software and a nice orchestral synthesizer that can create a rendition for you.