Lewis & Short

Tībur, ŭris, n., an ancient town of Latium on both sides of the Anio, now Tivoli: Tiburque superbum, Verg. A. 7, 630; Hor. C. 2, 6, 5: supinum, id. ib. 3, 4, 23: udum, id. ib. 3, 29, 6; id. Ep. 1, 8, 12; 2, 2, 3: pronum, Juv. 3, 192: vacuum, quiet, Mart. 1, 13, 1; 4, 64, 32.
Hence,

  1. A. Tīburs, urtis, adj., of or belonging to Tibur, Tiburtine: populus, Liv. 8, 12; cf.: SENATVS POPVLVSQVE TIBVRS, Inscr. Orell. 113 and 3728: hostis, Liv. 7, 11, 4: via, Hor. S. 1, 6, 108: moenia, Verg. A. 7, 670: poma, Hor. S. 2, 4, 70: Fauni, Stat. S. 1, 3, 99: bibliotheca, Gell. 19, 5, 4.
    Subst.: Tīburs, urtis, n., the Tiburtine territory: in Tiburti, Varr. R. R. 1, 9, 6; Cic. Att. 8, 14, 3; id. de Or. 2, 55, 224; for which: in Tiburte, Glaucia ap. Cic. de Or. 2, 65, 263; Gell. 19, 5, 1.
    In plur.: Tīburtes, um, m., the inhabitants of Tibur, the Tiburtines, Plin. 16, 44, 87, § 237; Liv. 7, 11; Tac. A. 14, 22 med.; Front. Aquaed. 6 and 66; Verg. A. 11, 757; Inscr. Orell. 1817; 2239; 3114; 3851.
  2. B. Tī-burtīnus, a, um, adj., of Tibur, Tiburtine: terra, Prop. 4 (5), 7, 85: oves, Mart. 7, 80, 12: ficus, Plin. 15, 18, 19, § 70: lapis, id. 36, 6, 5, § 46; 36, 22, 48, § 167: frigora, Mart. 4, 57, 10: Diana, id. 7, 28, 1: via, leading from the Esquiline gate towards Tibur, Plin. Ep. 7, 29, 2.
    Subst.: Tībur-tīnum, i, n., the Tiburtine villa (of Scipio): in Tiburtino Scipionis, Cic. Phil. 5, 7, 19; Sen. Ben. 4, 12, 4.
  3. C. Tīburnus, a, um, adj., of Tibur, Tiburtine: Anio, Prop. 3, 22, 23.
    Subst.: Tīburnus, i, m., an inhabitant of Tibur, a Tiburnian, Stat. S. 1, 3, 74; also, κατ’ ἐξοχήν, for Tiburtus, the founder of Tibur, Hor. C. 1, 7, 13.