£1,000 doesn't go all the way when buying a bass trombone. Single trigger you'll be able to get, which is good for most purposes. JP Rath are okay. Wessex are doing some interesting things with designs. £2,000 would get you most things, including some desirable items (e.g. the occasional Rath R9 that someone is keen to sell).
Quality 2nd hand is where the value is - you ought to be able to find a Bb/F instrument of desired size from medium-small tenor to bass for that budget. Single-trigger suggestions:
.508: King 3B/F
.525: King 3B+/F, Bach 36B, Conn 79H
.547: Conn 88H, King 4B/F, Bach 42B
.562 (bass): Conn 72H, Conn 70H, Conn 71H, Conn 110H, Bach 50B, Holton TR183
Then there are many double trigger bass models that might happen to pop down into your price bracket 2nd hand - Conn 62H, Bach 50B2, 50B3, Holton TR181, TR180, King 6B Duo Gravis, 7B, 8B, Benge 290, etc. You're basically looking for models that have been or were made for some decades that are or were standard designs for a reason. Forgive ugliness in a potential instrument - the outside is not important, but good cosmetic condition costs.