You still didn't answer to a lot of questions I've put here:
Note - latest AMX MOD X (I believe You are using this one) doesn't support 100% older CS version. Normally latest AMX MOD X is supposed to work with Steam and it's mods. There was a problem with recognizing bots/players by older version AMX X 0.16 (and also by AMX including latest official version 0.9.9), but in AMX X since version 0.20 the problem is fixed. I got to work AMX MOD X 1.01 with 100% (I believe) compatibility with CS1.5 (old HL) and without problems with bots, but I shoud've re-write few plugins to get back support for this old mod.
I don't know what are really the differences betwen CS1.5 (this one I have) and retail version (I believe You are using this one) CS 184.108.40.206. I may answer to a lot of questions to CS1.5 old HL / CS1.6 Steam and AMX or AMX MOD X, but since I don't have any experience with CS220.127.116.11 and AMX MOD X - I'am not sure if I can help You.
Hint - try to disable all custom plugins in Your amxx' plugins.ini and start the server only with default AMX X plugins and bots and look if it works for You with bots correctly (I mean check this amxmodmenu). If so - You can add step by step a custom plugin to the plugins.ini file and check if it stiil works. This way You may narrow some plugin not compatible with bots. If it doesn't work even with default AMX X plugins - I don't see any hope for You. I don't think the people from AMX MOD X will be interested to support old mods with correct recognize by AMX X bots and players by their mod.
Write also more precisly what exactly the function(s) You have been trying and they didn't work for You (these called by You from amxmodmenu).
BTW - @Pierre - is this topic in the correct forum? Also this one I've put link to my post in it few lines above?