Does the BBS limit the number of supervision hours I can claim? (MFT)

Yes!  Although the BBS does not directly limit the number of supervision hours logged, supervision hours are included within the non-counseling experience (NCE) category which has a maximum of 1,000 hours.  Once you hit the NCE category maximum additional supervision hours may not be claimed.  If you hit a category maximum TrackYourHours automatically subtracts additional hours logged in that category from your valid total so you always know how many you can actually claim.  Additionally, the BBS only allows you to claim 5 supervision hours in a single week.