well, guess who [sort of] started it, way back in 1596?!
(Dickens does seem to have been the first to put it together with bad rubbish, in 1847.)

riddance 5. a. A deliverance which consists in getting rid of something. Freq. with adjs., as good, happy. Also transf., something of which one gets rid.
1596–1676 [see b]. 1694 Kettlewell Comp. Persecuted 102 Give them comfort under their sufferings, and in thy due time an happy riddance thereof. 1827 Scott Jrnl. II. 4 God send honest industry a fair riddance. 1844 Thirlwall Greece VIII. lxii. 147 The loss of so many captives was treated as a happy riddance. 1861 Dickens Gt. Expect. xlii, Compeyson took it easy as a good riddance for both sides. 1867 I Dr. Marigold, His mother indignantly declared that a girl who could so conduct herself was indeed a good riddance.
b. In interjectional phr. a good (†fair, gentle) riddance. Also in phr. good riddance of (or to) bad rubbish.
1596 Shakes. Merch. V. ii. vii. 78 Portia adew.+ Por. A gentle riddance. c1613 Middleton No Wit like Woman's ii. iii, Low. They've given thee all the slip. Mis. Low. So, a fair riddance! 1676 G. Etherege Man of Mode ii. ii, Loveit. Call him again. Pert. E'n let him go, a fair riddance. 1742 Young Nt. Th. ii. 119 We+all expedients tire, To lash the ling'ring moments into speed, And whirl us (happy riddance!) from ourselves. 1782 E. N. Blower Geo. Bateman III. 7 In less time than whilst one could cry—‘A good riddance’. 1847 Dickens Dombey (1848) xliv. 438 A good riddance of bad rubbish!+ Get along with you, or I'll have you carried out! 1863 C. Reade Hard Cash xxxii, She is turned away—for sauce—and a good riddance of bad rubbish. 1883 ‘Annie Thomas’ Mod. Housewife 35 ‘As soon as his master comes home he shall go.’ ‘A good riddance too,’ she said morosely. 1924 M. Irwin Still she wished for Company xviii. 220 If all they say downstairs is true+it's good riddance to bad foreign rubbish. 1928 S. Sassoon Mem. Fox-Hunting Man viii. ii. 287 It may well be wondered how the Hunt had survived the despotism of the old-world grandee, with whom previous Masters had been obliged to cooperate (as ‘best Master we've ever had’ while they reigned, and ‘good riddance of bad rubbish’ when they resigned). 1975 Times 4 July 5/3 The American War of Independence+can be seen, as George III consoled himself by looking at it, as good riddance to bad rubbish. 1977 H. Fast Immigrants ii. 110 A dead Chinese was good riddance to bad rubbish.


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