As per my idea there is no any BBT exam is conducted by TOEFL. TOEFL is organised for IBT, PBT or CBT.

The TOEFL PBT test is administered in a paper-delivered format. This is currently offered only in locations where testing via the Internet is not available

Scores remain valid for 2 years after your test date.

More than 30 million people from all over the world have taken the TOEFL test to demonstrate their English-language proficiency.

More than 9,000 universities and colleges in over 130 countries accept TOEFL test scores.

Some Universities require minimum score of 250/600 (CBT/PBT), some have a requirement of 213 (CBT) or 550 (PBT).

Some require score of 115 (iBT) for TA/RA.

Internet Based Test (iBT) Computer Based Test (CBT) Paper Based Test (PBT)
120 300 677
120 297 673
119 293 670
118 290 667
117 287 660-663
116 283 657
114-115 280 650-653
113 277 647
111-112 273 640-643
110 270 637
109 267 630-633
106-108 263 623-627
105 260 617-620
103-104 257 613
101-102 253 607-610
100 250 600-603
98-99 247 597
96-97 243 590-593
94-95 240 587
92-93 237 580-583
90-91 233 577
88-89 230 570-573
86-87 227 567
84-85 223 563
83 220 557-560
81-82 217 553
79-80 213 550
77-78 210 547
76 207 540-543
74-75 203 537